System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=189, |B|=467, |A∩B|=163 (compute |A∪B|), then apply lcm to the result and 2.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 189 + 467 - 163 = 493. Then, The least common multiple of 493 and 2 is 986.
result = "986"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=113, |B|=224, |A∩B|=83 (compute |A∪B|), then apply lcm to the result and 19.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 113 + 224 - 83 = 254. Then, The least common multiple of 254 and 19 is 4826.
result = "4826"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=766, |B|=167, |A∩B|=71 (compute |A∪B|), then apply lcm to the result and 4.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 766 + 167 - 71 = 862. Then, The least common multiple of 862 and 4 is 1724.
result = "1724"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=772, |B|=254, |A∩B|=86 (compute |A∪B|), then apply lcm to the result and 50.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 772 + 254 - 86 = 940. Then, The least common multiple of 940 and 50 is 4700.
result = "4700"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=336, |B|=212, |A∩B|=153 (compute |A∪B|), then apply lcm to the result and 13.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 336 + 212 - 153 = 395. Then, The least common multiple of 395 and 13 is 5135.
result = "5135"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=614, |B|=378, |A∩B|=180 (compute |A∪B|), then apply lcm to the result and 42.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 614 + 378 - 180 = 812. Then, The least common multiple of 812 and 42 is 2436.
result = "2436"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=858, |B|=325, |A∩B|=200 (compute |A∪B|), then apply lcm to the result and 10.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 858 + 325 - 200 = 983. Then, The least common multiple of 983 and 10 is 9830.
result = "9830"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=240, |B|=943, |A∩B|=200 (compute |A∪B|), then apply lcm to the result and 3.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 240 + 943 - 200 = 983. Then, The least common multiple of 983 and 3 is 2949.
result = "2949"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=391, |B|=526, |A∩B|=174 (compute |A∪B|), then apply lcm to the result and 11.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 391 + 526 - 174 = 743. Then, The least common multiple of 743 and 11 is 8173.
result = "8173"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=344, |B|=474, |A∩B|=186 (compute |A∪B|), then apply lcm to the result and 3.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 344 + 474 - 186 = 632. Then, The least common multiple of 632 and 3 is 1896.
result = "1896"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=153, |B|=806, |A∩B|=120 (compute |A∪B|), then apply lcm to the result and 2.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 153 + 806 - 120 = 839. Then, The least common multiple of 839 and 2 is 1678.
result = "1678"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=182, |B|=176, |A∩B|=172 (compute |A∪B|), then apply lcm to the result and 41.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 182 + 176 - 172 = 186. Then, The least common multiple of 186 and 41 is 7626.
result = "7626"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=233, |B|=214, |A∩B|=124 (compute |A∪B|), then apply lcm to the result and 57.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 233 + 214 - 124 = 323. Then, The least common multiple of 323 and 57 is 969.
result = "969"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=285, |B|=543, |A∩B|=102 (compute |A∪B|), then apply lcm to the result and 15.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 285 + 543 - 102 = 726. Then, The least common multiple of 726 and 15 is 3630.
result = "3630"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=266, |B|=488, |A∩B|=33 (compute |A∪B|), then apply lcm to the result and 12.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 266 + 488 - 33 = 721. Then, The least common multiple of 721 and 12 is 8652.
result = "8652"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=141, |B|=274, |A∩B|=118 (compute |A∪B|), then apply lcm to the result and 57.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 141 + 274 - 118 = 297. Then, The least common multiple of 297 and 57 is 5643.
result = "5643"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=650, |B|=186, |A∩B|=152 (compute |A∪B|), then apply lcm to the result and 14.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 650 + 186 - 152 = 684. Then, The least common multiple of 684 and 14 is 4788.
result = "4788"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=308, |B|=536, |A∩B|=185 (compute |A∪B|), then apply lcm to the result and 9.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 308 + 536 - 185 = 659. Then, The least common multiple of 659 and 9 is 5931.
result = "5931"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=351, |B|=363, |A∩B|=91 (compute |A∪B|), then apply lcm to the result and 4.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 351 + 363 - 91 = 623. Then, The least common multiple of 623 and 4 is 2492.
result = "2492"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=695, |B|=257, |A∩B|=103 (compute |A∪B|), then apply lcm to the result and 21.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 695 + 257 - 103 = 849. Then, The least common multiple of 849 and 21 is 5943.
result = "5943"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=548, |B|=385, |A∩B|=176 (compute |A∪B|), then apply lcm to the result and 4.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 548 + 385 - 176 = 757. Then, The least common multiple of 757 and 4 is 3028.
result = "3028"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=617, |B|=325, |A∩B|=182 (compute |A∪B|), then apply lcm to the result and 72.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 617 + 325 - 182 = 760. Then, The least common multiple of 760 and 72 is 6840.
result = "6840"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=467, |B|=495, |A∩B|=173 (compute |A∪B|), then apply lcm to the result and 27.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 467 + 495 - 173 = 789. Then, The least common multiple of 789 and 27 is 7101.
result = "7101"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=513, |B|=101, |A∩B|=39 (compute |A∪B|), then apply lcm to the result and 6.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 513 + 101 - 39 = 575. Then, The least common multiple of 575 and 6 is 3450.
result = "3450"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=661, |B|=285, |A∩B|=138 (compute |A∪B|), then apply lcm to the result and 18.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 661 + 285 - 138 = 808. Then, The least common multiple of 808 and 18 is 7272.
result = "7272"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=123, |B|=334, |A∩B|=26 (compute |A∪B|), then apply lcm to the result and 2.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 123 + 334 - 26 = 431. Then, The least common multiple of 431 and 2 is 862.
result = "862"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=131, |B|=84, |A∩B|=67 (compute |A∪B|), then apply lcm to the result and 5.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 131 + 84 - 67 = 148. Then, The least common multiple of 148 and 5 is 740.
result = "740"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=508, |B|=597, |A∩B|=199 (compute |A∪B|), then apply lcm to the result and 48.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 508 + 597 - 199 = 906. Then, The least common multiple of 906 and 48 is 7248.
result = "7248"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=201, |B|=81, |A∩B|=79 (compute |A∪B|), then apply lcm to the result and 33.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 201 + 81 - 79 = 203. Then, The least common multiple of 203 and 33 is 6699.
result = "6699"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=99, |B|=92, |A∩B|=68 (compute |A∪B|), then apply lcm to the result and 99.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 99 + 92 - 68 = 123. Then, The least common multiple of 123 and 99 is 4059.
result = "4059"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=754, |B|=202, |A∩B|=82 (compute |A∪B|), then apply lcm to the result and 20.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 754 + 202 - 82 = 874. Then, The least common multiple of 874 and 20 is 8740.
result = "8740"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=312, |B|=242, |A∩B|=146 (compute |A∪B|), then apply lcm to the result and 19.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 312 + 242 - 146 = 408. Then, The least common multiple of 408 and 19 is 7752.
result = "7752"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=411, |B|=205, |A∩B|=156 (compute |A∪B|), then apply lcm to the result and 26.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 411 + 205 - 156 = 460. Then, The least common multiple of 460 and 26 is 5980.
result = "5980"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=292, |B|=167, |A∩B|=108 (compute |A∪B|), then apply lcm to the result and 99.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 292 + 167 - 108 = 351. Then, The least common multiple of 351 and 99 is 3861.
result = "3861"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=756, |B|=374, |A∩B|=173 (compute |A∪B|), then apply lcm to the result and 66.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 756 + 374 - 173 = 957. Then, The least common multiple of 957 and 66 is 1914.
result = "1914"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=446, |B|=719, |A∩B|=187 (compute |A∪B|), then apply lcm to the result and 8.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 446 + 719 - 187 = 978. Then, The least common multiple of 978 and 8 is 3912.
result = "3912"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=206, |B|=264, |A∩B|=89 (compute |A∪B|), then apply lcm to the result and 10.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 206 + 264 - 89 = 381. Then, The least common multiple of 381 and 10 is 3810.
result = "3810"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=278, |B|=504, |A∩B|=67 (compute |A∪B|), then apply lcm to the result and 8.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 278 + 504 - 67 = 715. Then, The least common multiple of 715 and 8 is 5720.
result = "5720"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=147, |B|=447, |A∩B|=34 (compute |A∪B|), then apply lcm to the result and 3.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 147 + 447 - 34 = 560. Then, The least common multiple of 560 and 3 is 1680.
result = "1680"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=159, |B|=437, |A∩B|=131 (compute |A∪B|), then apply lcm to the result and 51.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 159 + 437 - 131 = 465. Then, The least common multiple of 465 and 51 is 7905.
result = "7905"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=307, |B|=243, |A∩B|=65 (compute |A∪B|), then apply lcm to the result and 60.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 307 + 243 - 65 = 485. Then, The least common multiple of 485 and 60 is 5820.
result = "5820"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=390, |B|=431, |A∩B|=86 (compute |A∪B|), then apply lcm to the result and 77.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 390 + 431 - 86 = 735. Then, The least common multiple of 735 and 77 is 8085.
result = "8085"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=183, |B|=529, |A∩B|=111 (compute |A∪B|), then apply lcm to the result and 3.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 183 + 529 - 111 = 601. Then, The least common multiple of 601 and 3 is 1803.
result = "1803"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=354, |B|=305, |A∩B|=161 (compute |A∪B|), then apply lcm to the result and 36.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 354 + 305 - 161 = 498. Then, The least common multiple of 498 and 36 is 2988.
result = "2988"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=472, |B|=354, |A∩B|=182 (compute |A∪B|), then apply lcm to the result and 13.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 472 + 354 - 182 = 644. Then, The least common multiple of 644 and 13 is 8372.
result = "8372"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=226, |B|=432, |A∩B|=200 (compute |A∪B|), then apply lcm to the result and 11.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 226 + 432 - 200 = 458. Then, The least common multiple of 458 and 11 is 5038.
result = "5038"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=335, |B|=302, |A∩B|=179 (compute |A∪B|), then apply lcm to the result and 18.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 335 + 302 - 179 = 458. Then, The least common multiple of 458 and 18 is 4122.
result = "4122"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=214, |B|=245, |A∩B|=109 (compute |A∪B|), then apply lcm to the result and 3.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 214 + 245 - 109 = 350. Then, The least common multiple of 350 and 3 is 1050.
result = "1050"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=797, |B|=205, |A∩B|=200 (compute |A∪B|), then apply lcm to the result and 8.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 797 + 205 - 200 = 802. Then, The least common multiple of 802 and 8 is 3208.
result = "3208"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=594, |B|=523, |A∩B|=190 (compute |A∪B|), then apply lcm to the result and 8.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 594 + 523 - 190 = 927. Then, The least common multiple of 927 and 8 is 7416.
result = "7416"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=481, |B|=326, |A∩B|=153 (compute |A∪B|), then apply lcm to the result and 66.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 481 + 326 - 153 = 654. Then, The least common multiple of 654 and 66 is 7194.
result = "7194"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=124, |B|=246, |A∩B|=66 (compute |A∪B|), then apply lcm to the result and 25.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 124 + 246 - 66 = 304. Then, The least common multiple of 304 and 25 is 7600.
result = "7600"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=322, |B|=312, |A∩B|=82 (compute |A∪B|), then apply lcm to the result and 30.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 322 + 312 - 82 = 552. Then, The least common multiple of 552 and 30 is 2760.
result = "2760"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=125, |B|=859, |A∩B|=79 (compute |A∪B|), then apply lcm to the result and 25.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 125 + 859 - 79 = 905. Then, The least common multiple of 905 and 25 is 4525.
result = "4525"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=679, |B|=248, |A∩B|=44 (compute |A∪B|), then apply lcm to the result and 4.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 679 + 248 - 44 = 883. Then, The least common multiple of 883 and 4 is 3532.
result = "3532"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=444, |B|=271, |A∩B|=89 (compute |A∪B|), then apply lcm to the result and 28.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 444 + 271 - 89 = 626. Then, The least common multiple of 626 and 28 is 8764.
result = "8764"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=154, |B|=128, |A∩B|=119 (compute |A∪B|), then apply lcm to the result and 5.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 154 + 128 - 119 = 163. Then, The least common multiple of 163 and 5 is 815.
result = "815"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=575, |B|=191, |A∩B|=134 (compute |A∪B|), then apply lcm to the result and 80.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 575 + 191 - 134 = 632. Then, The least common multiple of 632 and 80 is 6320.
result = "6320"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=534, |B|=479, |A∩B|=146 (compute |A∪B|), then apply lcm to the result and 18.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 534 + 479 - 146 = 867. Then, The least common multiple of 867 and 18 is 5202.
result = "5202"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=246, |B|=332, |A∩B|=156 (compute |A∪B|), then apply lcm to the result and 8.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 246 + 332 - 156 = 422. Then, The least common multiple of 422 and 8 is 1688.
result = "1688"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=170, |B|=459, |A∩B|=132 (compute |A∪B|), then apply lcm to the result and 20.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 170 + 459 - 132 = 497. Then, The least common multiple of 497 and 20 is 9940.
result = "9940"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=270, |B|=159, |A∩B|=118 (compute |A∪B|), then apply lcm to the result and 12.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 270 + 159 - 118 = 311. Then, The least common multiple of 311 and 12 is 3732.
result = "3732"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=443, |B|=605, |A∩B|=200 (compute |A∪B|), then apply lcm to the result and 14.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 443 + 605 - 200 = 848. Then, The least common multiple of 848 and 14 is 5936.
result = "5936"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=383, |B|=132, |A∩B|=22 (compute |A∪B|), then apply lcm to the result and 11.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 383 + 132 - 22 = 493. Then, The least common multiple of 493 and 11 is 5423.
result = "5423"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=402, |B|=291, |A∩B|=43 (compute |A∪B|), then apply lcm to the result and 78.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 402 + 291 - 43 = 650. Then, The least common multiple of 650 and 78 is 1950.
result = "1950"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=211, |B|=596, |A∩B|=196 (compute |A∪B|), then apply lcm to the result and 6.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 211 + 596 - 196 = 611. Then, The least common multiple of 611 and 6 is 3666.
result = "3666"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=81, |B|=82, |A∩B|=22 (compute |A∪B|), then apply lcm to the result and 72.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 81 + 82 - 22 = 141. Then, The least common multiple of 141 and 72 is 3384.
result = "3384"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=238, |B|=327, |A∩B|=109 (compute |A∪B|), then apply lcm to the result and 54.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 238 + 327 - 109 = 456. Then, The least common multiple of 456 and 54 is 4104.
result = "4104"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=170, |B|=171, |A∩B|=160 (compute |A∪B|), then apply lcm to the result and 2.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 170 + 171 - 160 = 181. Then, The least common multiple of 181 and 2 is 362.
result = "362"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=275, |B|=213, |A∩B|=199 (compute |A∪B|), then apply lcm to the result and 5.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 275 + 213 - 199 = 289. Then, The least common multiple of 289 and 5 is 1445.
result = "1445"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=134, |B|=134, |A∩B|=107 (compute |A∪B|), then apply lcm to the result and 38.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 134 + 134 - 107 = 161. Then, The least common multiple of 161 and 38 is 6118.
result = "6118"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=223, |B|=314, |A∩B|=54 (compute |A∪B|), then apply lcm to the result and 36.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 223 + 314 - 54 = 483. Then, The least common multiple of 483 and 36 is 5796.
result = "5796"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=448, |B|=257, |A∩B|=21 (compute |A∪B|), then apply lcm to the result and 40.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 448 + 257 - 21 = 684. Then, The least common multiple of 684 and 40 is 6840.
result = "6840"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=381, |B|=294, |A∩B|=135 (compute |A∪B|), then apply lcm to the result and 85.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 381 + 294 - 135 = 540. Then, The least common multiple of 540 and 85 is 9180.
result = "9180"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=406, |B|=130, |A∩B|=48 (compute |A∪B|), then apply lcm to the result and 32.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 406 + 130 - 48 = 488. Then, The least common multiple of 488 and 32 is 1952.
result = "1952"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=323, |B|=201, |A∩B|=175 (compute |A∪B|), then apply lcm to the result and 17.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 323 + 201 - 175 = 349. Then, The least common multiple of 349 and 17 is 5933.
result = "5933"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=215, |B|=282, |A∩B|=161 (compute |A∪B|), then apply lcm to the result and 51.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 215 + 282 - 161 = 336. Then, The least common multiple of 336 and 51 is 5712.
result = "5712"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=384, |B|=112, |A∩B|=43 (compute |A∪B|), then apply lcm to the result and 60.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 384 + 112 - 43 = 453. Then, The least common multiple of 453 and 60 is 9060.
result = "9060"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=80, |B|=92, |A∩B|=38 (compute |A∪B|), then apply lcm to the result and 60.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 80 + 92 - 38 = 134. Then, The least common multiple of 134 and 60 is 4020.
result = "4020"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=315, |B|=434, |A∩B|=177 (compute |A∪B|), then apply lcm to the result and 48.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 315 + 434 - 177 = 572. Then, The least common multiple of 572 and 48 is 6864.
result = "6864"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=155, |B|=227, |A∩B|=128 (compute |A∪B|), then apply lcm to the result and 21.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 155 + 227 - 128 = 254. Then, The least common multiple of 254 and 21 is 5334.
result = "5334"


System: You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[System] You are a precise operations engine. Apply the named operations exactly, in order, and end with result = "<answer>".

[User]
Apply venn to the sets |A|=88, |B|=84, |A∩B|=52 (compute |A∪B|), then apply lcm to the result and 58.
Show your working, then end with:
result = "<...>"

Response:
|A ∪ B| = |A| + |B| - |A∩B| = 88 + 84 - 52 = 120. Then, The least common multiple of 120 and 58 is 3480.
result = "3480"