diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/11762.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/11762.txt new file mode 100644 index 0000000000000000000000000000000000000000..15b59b71708b8d47299c245a02a8283017bdc29f --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/11762.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${2401, 25, 64, 4096, 5}$. +Answer: +$8\ 7^{4/5} 10^{3/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/13703.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/13703.txt new file mode 100644 index 0000000000000000000000000000000000000000..59ca06096a7681be2d13f6300cb57f1def54d876 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/13703.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${625, 256, 6, -1, -512}$. +Answer: +$8\ 2^{3/5} \sqrt[5]{3} 5^{4/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/13834.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/13834.txt new file mode 100644 index 0000000000000000000000000000000000000000..f92c0621e27ad05f86848817fd0561859f8c0ddb --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/13834.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${-1000, 100, 4096, 9, 243, 8}$. +Answer: +$24 \sqrt[6]{-3} \sqrt[3]{2} 5^{5/6}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/14448.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/14448.txt new file mode 100644 index 0000000000000000000000000000000000000000..e46cda2efe5842dbb69e3e82d238b34755fba833 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/14448.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${1, 1, -512, -7776, 1}$. +Answer: +$12\ 2^{4/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/14876.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/14876.txt new file mode 100644 index 0000000000000000000000000000000000000000..e7fa51ea1d3a8eff455cd7e01660b25c5cf28c53 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/14876.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${25, 3}$. +Answer: +$5 \sqrt{3}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/15313.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/15313.txt new file mode 100644 index 0000000000000000000000000000000000000000..ea21e867c8e72df53567a3e4427b6f65269d60ca --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/15313.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${64, 7, 36}$. +Answer: +$4\ 6^{2/3} \sqrt[3]{7}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/15655.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/15655.txt new file mode 100644 index 0000000000000000000000000000000000000000..c339a5307bac481e1975e4838935e3cc2767db48 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/15655.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${9, 16807, 343, 243, 36}$. +Answer: +$21\ 2^{2/5} 3^{4/5} 7^{3/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/21408.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/21408.txt new file mode 100644 index 0000000000000000000000000000000000000000..dcf244d5e7b2eece875171ae145cf23ec7d5eeb9 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/21408.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${-10, -125, 1, 9, 10000}$. +Answer: +$10\ 3^{2/5} 5^{3/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/24752.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/24752.txt new file mode 100644 index 0000000000000000000000000000000000000000..caf22da8213823244bb4b8512928c8721d20fac4 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/24752.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${64, 15625, 625, -7776, 256, 81}$. +Answer: +$120 \sqrt[6]{-2} \sqrt{3} 5^{2/3}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/26452.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/26452.txt new file mode 100644 index 0000000000000000000000000000000000000000..808a15badcdbab1f57e18c7465caad8710be97bc --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/26452.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${81, 4, 1, 625}$. +Answer: +$15 \sqrt{2}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/29009.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/29009.txt new file mode 100644 index 0000000000000000000000000000000000000000..6380f64d2b202d0eb41679292262359ed9f17e63 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/29009.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${-27, 36, -3}$. +Answer: +$9\ 2^{2/3}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/29565.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/29565.txt new file mode 100644 index 0000000000000000000000000000000000000000..99809ec98f83f1c36282fcc0dd78f9bf4417a964 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/29565.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${-64, 1000, 9}$. +Answer: +$40 \sqrt[3]{-1} 3^{2/3}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/30398.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/30398.txt new file mode 100644 index 0000000000000000000000000000000000000000..c4dada27d9519b3758cea462923c29cec7fdab70 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/30398.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${-5, 49, 16}$. +Answer: +$2 \sqrt[3]{-10} 7^{2/3}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/31737.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/31737.txt new file mode 100644 index 0000000000000000000000000000000000000000..a675fd8072e5f8384c7ad236b6a218197899be74 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/31737.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${256, 36, 49, -59049, 64}$. +Answer: +$72 \sqrt[5]{-2} 21^{2/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/31745.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/31745.txt new file mode 100644 index 0000000000000000000000000000000000000000..b98235c863b49af618467baee7e84e1bd9a05217 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/31745.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${8, -2, -7}$. +Answer: +$2 \sqrt[3]{14}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/33464.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/33464.txt new file mode 100644 index 0000000000000000000000000000000000000000..4d0d78866f087e1f0cf6f8e5a585671d73761a97 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/33464.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${512, 16, 7, 81, -7776}$. +Answer: +$24 \sqrt[5]{-7} 2^{3/5} 3^{4/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/36331.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/36331.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4163eb2bbbe47555ce005b9c16e8f821d1f4289 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/36331.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${36, 16807, 216, 1, -7776, 117649}$. +Answer: +$42 \sqrt[6]{-1} 6^{2/3} 7^{5/6}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/37381.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/37381.txt new file mode 100644 index 0000000000000000000000000000000000000000..c9de87280eeaa8ccd92e079c3fe6e65c3261b391 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/37381.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${1, 16, 5}$. +Answer: +$2 \sqrt[3]{10}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/38512.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/38512.txt new file mode 100644 index 0000000000000000000000000000000000000000..f00d2502d26f4c2b98d1b30cda0da290ad880a20 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/38512.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${25, -59049, 16, 25, 25}$. +Answer: +$45 \sqrt[5]{-5} 2^{4/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/39370.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/39370.txt new file mode 100644 index 0000000000000000000000000000000000000000..0a6cca3c85b29bea49c6fdd7338969af026f9f40 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/39370.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${1, 1296, 512, -27}$. +Answer: +$(12+12 i) 6^{3/4}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/42387.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/42387.txt new file mode 100644 index 0000000000000000000000000000000000000000..b5b681dec8edf37f0043dc28b712451f8696db8c --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/42387.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${81, 10, 3}$. +Answer: +$3\ 3^{2/3} \sqrt[3]{10}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/44105.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/44105.txt new file mode 100644 index 0000000000000000000000000000000000000000..710a2b073761cd5dd1793368d1b471c5e692730a --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/44105.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${49, -16807, 64, 36, 81, 3}$. +Answer: +$42 \sqrt[6]{-21} \sqrt[3]{2}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/44567.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/44567.txt new file mode 100644 index 0000000000000000000000000000000000000000..5cd9021d0e9a4eb702d4c149f2535fb2961959c6 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/44567.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${-512, 625, -10, 49}$. +Answer: +$20 \sqrt[4]{5} \sqrt{14}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/45249.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/45249.txt new file mode 100644 index 0000000000000000000000000000000000000000..610ddf001af2f9654ca82f362f1ad7e5d96dd977 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/45249.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${3, 3, 64, 9}$. +Answer: +$6 \sqrt{2}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/49885.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/49885.txt new file mode 100644 index 0000000000000000000000000000000000000000..302c418b01bbf7d1a455dd3b70be38ddcfa19b8d --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/49885.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${10, 1}$. +Answer: +$\sqrt{10}$ \ No newline at end of file diff --git a/pretraining/mathematica/counting_and_statistics/geometric_mean/6079.txt b/pretraining/mathematica/counting_and_statistics/geometric_mean/6079.txt new file mode 100644 index 0000000000000000000000000000000000000000..954d9e2a681f0a98a4b7734fa2327c12f6c9f6a5 --- /dev/null +++ b/pretraining/mathematica/counting_and_statistics/geometric_mean/6079.txt @@ -0,0 +1,4 @@ +Problem: +Compute the geometric mean of ${16, -6, -1, 343, 8}$. +Answer: +$2 \sqrt[5]{3} 14^{3/5}$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/13310.txt b/pretraining/mathematica/number_theory/lcm/13310.txt new file mode 100644 index 0000000000000000000000000000000000000000..984738875199b4bcdadbbf717c5e7ea1c7c9ecf5 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/13310.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{1,-\frac{14}{9},4\right\}$. +Answer: +$28$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/14085.txt b/pretraining/mathematica/number_theory/lcm/14085.txt new file mode 100644 index 0000000000000000000000000000000000000000..e836c95ed8c52a099c9edee704d86e77eb1e8925 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/14085.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-2,-\frac{11}{3}\right\}$. +Answer: +$22$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/1419.txt b/pretraining/mathematica/number_theory/lcm/1419.txt new file mode 100644 index 0000000000000000000000000000000000000000..897c07e7331ccc3e502b2822dcbdfb1488148182 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/1419.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{0,4,2,\frac{4}{3}\right\}$. +Answer: +$0$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/15377.txt b/pretraining/mathematica/number_theory/lcm/15377.txt new file mode 100644 index 0000000000000000000000000000000000000000..e851e823940e1b403a3883c53393c49616043a3f --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/15377.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{8}{3},-4\right\}$. +Answer: +$8$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/15766.txt b/pretraining/mathematica/number_theory/lcm/15766.txt new file mode 100644 index 0000000000000000000000000000000000000000..5b087077d5c7fd38a48af41daf474d9441322e3c --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/15766.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{10}{3},1,5,3\right\}$. +Answer: +$30$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/15944.txt b/pretraining/mathematica/number_theory/lcm/15944.txt new file mode 100644 index 0000000000000000000000000000000000000000..1f2f699073bfe1098b6e7bdd80afa274f88558f0 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/15944.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{5}{2},\frac{13}{9},\frac{22}{9}\right\}$. +Answer: +$1430$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/16502.txt b/pretraining/mathematica/number_theory/lcm/16502.txt new file mode 100644 index 0000000000000000000000000000000000000000..7697bbf6c72175cc6353a8e8c2232f49f5a233cc --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/16502.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{0,-1\}$. +Answer: +$0$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/1695.txt b/pretraining/mathematica/number_theory/lcm/1695.txt new file mode 100644 index 0000000000000000000000000000000000000000..2ef545372c223c83b967d72e39bdddb046abe633 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/1695.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{10}{3},-\frac{11}{3},1\right\}$. +Answer: +$110$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/17107.txt b/pretraining/mathematica/number_theory/lcm/17107.txt new file mode 100644 index 0000000000000000000000000000000000000000..e21c4ef76f1aa9da02cb361ba7b677c1789eff62 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/17107.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{12}{7},1,0,-5\right\}$. +Answer: +$0$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/17109.txt b/pretraining/mathematica/number_theory/lcm/17109.txt new file mode 100644 index 0000000000000000000000000000000000000000..04c5c3bf9724485a497b6de892ab4acf3d586f62 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/17109.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{14}{5},-1,2\right\}$. +Answer: +$14$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/1743.txt b/pretraining/mathematica/number_theory/lcm/1743.txt new file mode 100644 index 0000000000000000000000000000000000000000..0cde09a7a566f4fb4e9029927da7eb21c77386ae --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/1743.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{-4,4,-1,4\}$. +Answer: +$4$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/17546.txt b/pretraining/mathematica/number_theory/lcm/17546.txt new file mode 100644 index 0000000000000000000000000000000000000000..2cfe7f4d2ee4ba7c9243193a30e2a2406c3fa7e0 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/17546.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{-3,5,1,4\}$. +Answer: +$60$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/20173.txt b/pretraining/mathematica/number_theory/lcm/20173.txt new file mode 100644 index 0000000000000000000000000000000000000000..00989fe4ca4044bd87f3e466afc852511cf38e20 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/20173.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{38}{9},\frac{6}{5},0\right\}$. +Answer: +$0$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/20877.txt b/pretraining/mathematica/number_theory/lcm/20877.txt new file mode 100644 index 0000000000000000000000000000000000000000..ca26f2735311733f37de36970e321d0bf3622c6b --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/20877.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{2,-\frac{4}{7}\right\}$. +Answer: +$4$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/21339.txt b/pretraining/mathematica/number_theory/lcm/21339.txt new file mode 100644 index 0000000000000000000000000000000000000000..80e319f88bb00e572ba3a92b5cacb2e482c1b0d0 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/21339.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{5,\frac{31}{9},3\right\}$. +Answer: +$465$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/22241.txt b/pretraining/mathematica/number_theory/lcm/22241.txt new file mode 100644 index 0000000000000000000000000000000000000000..94d1dbad0d0bef08a7b9354c441d368ff0cb8ec1 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/22241.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{29}{9},3,-1,-1\right\}$. +Answer: +$87$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/22415.txt b/pretraining/mathematica/number_theory/lcm/22415.txt new file mode 100644 index 0000000000000000000000000000000000000000..54b5827573bbb745bf3334386658be28a16350bc --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/22415.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{5,-2\}$. +Answer: +$10$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/22659.txt b/pretraining/mathematica/number_theory/lcm/22659.txt new file mode 100644 index 0000000000000000000000000000000000000000..4f72dba3263009b5b1de0cdec7de445e37c68bd5 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/22659.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-4,-\frac{5}{2}\right\}$. +Answer: +$20$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/23706.txt b/pretraining/mathematica/number_theory/lcm/23706.txt new file mode 100644 index 0000000000000000000000000000000000000000..9c64b973600ded543499454e4eea1168d6ceaa99 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/23706.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{1,-\frac{35}{9}\right\}$. +Answer: +$35$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/24349.txt b/pretraining/mathematica/number_theory/lcm/24349.txt new file mode 100644 index 0000000000000000000000000000000000000000..9a229ca705ae8beace48f890864eb5b08cb4f3dd --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/24349.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{-3,0,4\}$. +Answer: +$0$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/25144.txt b/pretraining/mathematica/number_theory/lcm/25144.txt new file mode 100644 index 0000000000000000000000000000000000000000..9ac8632a2a01fd27b7a77f25e28c158e45d27cc6 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/25144.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-3,-2,-\frac{31}{7}\right\}$. +Answer: +$186$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/25206.txt b/pretraining/mathematica/number_theory/lcm/25206.txt new file mode 100644 index 0000000000000000000000000000000000000000..db676eeef3e747f0b1a514c29fac4a6049a5617e --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/25206.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{-5,-5\}$. +Answer: +$5$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/26121.txt b/pretraining/mathematica/number_theory/lcm/26121.txt new file mode 100644 index 0000000000000000000000000000000000000000..436b194d987f07abeb6e08318e398cad21d7171a --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/26121.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{5}{2},-3,3\right\}$. +Answer: +$15$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/26778.txt b/pretraining/mathematica/number_theory/lcm/26778.txt new file mode 100644 index 0000000000000000000000000000000000000000..d2e174de2cb319a7be3899f825ef8b492e462e8c --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/26778.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-3,-1,-\frac{9}{2},0\right\}$. +Answer: +$0$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/28137.txt b/pretraining/mathematica/number_theory/lcm/28137.txt new file mode 100644 index 0000000000000000000000000000000000000000..73c03a2bcfb9eee6ab7a9aa4fcdb02d8ab9cf1c7 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/28137.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-4,-\frac{7}{5}\right\}$. +Answer: +$28$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/30587.txt b/pretraining/mathematica/number_theory/lcm/30587.txt new file mode 100644 index 0000000000000000000000000000000000000000..a598ab6691d574b223b3695ecc6847c2100bac8f --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/30587.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{-3-i,3-i\}$. +Answer: +$5+5 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/32580.txt b/pretraining/mathematica/number_theory/lcm/32580.txt new file mode 100644 index 0000000000000000000000000000000000000000..026e77f4554e040ce0fb157b242766e1399dfbbd --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/32580.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{3 i,3,\frac{12}{5}+\frac{7 i}{5}\right\}$. +Answer: +$36+21 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/35225.txt b/pretraining/mathematica/number_theory/lcm/35225.txt new file mode 100644 index 0000000000000000000000000000000000000000..db54ee6889861a233b89f8a066fa3587402cd1ac --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/35225.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-2 i,-2+\frac{5 i}{3}\right\}$. +Answer: +$10+12 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/3528.txt b/pretraining/mathematica/number_theory/lcm/3528.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d2fd9c0d575b65f878f9bae8968f6f77aba16f5 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/3528.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{0,-2\}$. +Answer: +$0$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/35710.txt b/pretraining/mathematica/number_theory/lcm/35710.txt new file mode 100644 index 0000000000000000000000000000000000000000..48c6f8c751d27533789dfcc2a1968e99f5feb175 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/35710.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{11}{5}-\frac{2 i}{5},2-2 i,-1+\frac{4 i}{3},2 i\right\}$. +Answer: +$2+14 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/3625.txt b/pretraining/mathematica/number_theory/lcm/3625.txt new file mode 100644 index 0000000000000000000000000000000000000000..8b41cf4d96e11cf93f889b186cc7b6386611d331 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/3625.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{3,-\frac{43}{9},-1\right\}$. +Answer: +$129$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/36433.txt b/pretraining/mathematica/number_theory/lcm/36433.txt new file mode 100644 index 0000000000000000000000000000000000000000..51061d93f8780056a9078ccf0f0e98c0cc7ce95d --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/36433.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{2}{3}+\frac{i}{3},3+i,-\frac{8}{3}\right\}$. +Answer: +$8+16 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/36751.txt b/pretraining/mathematica/number_theory/lcm/36751.txt new file mode 100644 index 0000000000000000000000000000000000000000..79b07fce10d7aa2909a998598db18675386f99e2 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/36751.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{3-3 i,1-2 i,-2 i,-1-2 i\}$. +Answer: +$30$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/37157.txt b/pretraining/mathematica/number_theory/lcm/37157.txt new file mode 100644 index 0000000000000000000000000000000000000000..6cf3559f54d22788f79af4e94ba11019aae5d853 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/37157.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{5}{2}-\frac{3 i}{2},-\frac{9}{5}-\frac{9 i}{5}\right\}$. +Answer: +$45+27 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/37888.txt b/pretraining/mathematica/number_theory/lcm/37888.txt new file mode 100644 index 0000000000000000000000000000000000000000..11004a7141517ecc77da6dfb31bc31e7edce5905 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/37888.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{2-\frac{14 i}{5},\frac{11}{5}+\frac{11 i}{5},2-i\right\}$. +Answer: +$418+66 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/38949.txt b/pretraining/mathematica/number_theory/lcm/38949.txt new file mode 100644 index 0000000000000000000000000000000000000000..1c8258412d75958284b5b82b0c9b1fc2a1f91bf6 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/38949.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{11}{5}-\frac{13 i}{5},-1-3 i,3+i\right\}$. +Answer: +$35+15 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/39461.txt b/pretraining/mathematica/number_theory/lcm/39461.txt new file mode 100644 index 0000000000000000000000000000000000000000..7e7b5d47620ed1a00b89bbc880ce6334a4f23440 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/39461.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-3,2-i,2-3 i,-\frac{4}{3}+\frac{5 i}{3}\right\}$. +Answer: +$108+111 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/40260.txt b/pretraining/mathematica/number_theory/lcm/40260.txt new file mode 100644 index 0000000000000000000000000000000000000000..48ccfc97bbaa70a8f9ee571f2b07050b8ecfc6b2 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/40260.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\{-1,1,1+3 i\}$. +Answer: +$1+3 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/40492.txt b/pretraining/mathematica/number_theory/lcm/40492.txt new file mode 100644 index 0000000000000000000000000000000000000000..157c6634864f70dd6ffb74c559d567c7976c3efc --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/40492.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{5}{2}+i,-3+i,\frac{2}{3}+i,\frac{1}{2}-\frac{5 i}{2}\right\}$. +Answer: +$59+17 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/44008.txt b/pretraining/mathematica/number_theory/lcm/44008.txt new file mode 100644 index 0000000000000000000000000000000000000000..bc22b0ef5c2d185ec3e3edbd0c466c9fbb67ab4f --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/44008.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{2+\frac{3 i}{2},1+3 i,\frac{5}{3}+\frac{8 i}{3}\right\}$. +Answer: +$35+145 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/44134.txt b/pretraining/mathematica/number_theory/lcm/44134.txt new file mode 100644 index 0000000000000000000000000000000000000000..b4f264b5506491b1d97e918a1e7db79f14868b3a --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/44134.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{7}{5}-\frac{4 i}{5},\frac{6}{5}-\frac{8 i}{5}\right\}$. +Answer: +$16+2 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/44812.txt b/pretraining/mathematica/number_theory/lcm/44812.txt new file mode 100644 index 0000000000000000000000000000000000000000..8b137922664f86f607d0dcf3e47d330e71fef6dc --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/44812.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-3-\frac{2 i}{3},-\frac{1}{5}-\frac{6 i}{5},-3+i\right\}$. +Answer: +$53+59 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/45919.txt b/pretraining/mathematica/number_theory/lcm/45919.txt new file mode 100644 index 0000000000000000000000000000000000000000..56c877f0a7c42a631e1e32dbd2f2dca69fc48e30 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/45919.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{1}{5}+\frac{13 i}{5},2 i,-\frac{6}{5}-i,-\frac{3}{2}-2 i\right\}$. +Answer: +$62+316 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/46804.txt b/pretraining/mathematica/number_theory/lcm/46804.txt new file mode 100644 index 0000000000000000000000000000000000000000..be877972c7d09bcaebfc1cc839d8cc37c6663f53 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/46804.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{3 i,1+i,3-\frac{i}{2}\right\}$. +Answer: +$21+15 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/47399.txt b/pretraining/mathematica/number_theory/lcm/47399.txt new file mode 100644 index 0000000000000000000000000000000000000000..e9edb50f92ae5d4ee1a7d6875cd65f0193fe44e9 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/47399.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{1}{2}+\frac{3 i}{2},\frac{12}{5}+\frac{9 i}{5},2-3 i\right\}$. +Answer: +$45+30 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/554.txt b/pretraining/mathematica/number_theory/lcm/554.txt new file mode 100644 index 0000000000000000000000000000000000000000..b443ac336bdd2daeb050342776d4eb15ee54afbf --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/554.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-3,-2,-\frac{3}{5},-1\right\}$. +Answer: +$6$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/6738.txt b/pretraining/mathematica/number_theory/lcm/6738.txt new file mode 100644 index 0000000000000000000000000000000000000000..3658d3e33ada87615d90b96229f8daecb2ed31e8 --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/6738.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{4}{5}-\frac{6 i}{5},2 i,-1-i,-\frac{3}{5}-\frac{14 i}{5}\right\}$. +Answer: +$4+46 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/8603.txt b/pretraining/mathematica/number_theory/lcm/8603.txt new file mode 100644 index 0000000000000000000000000000000000000000..2196c1b414f8557f0317587534151db838eecd4c --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/8603.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{\frac{2}{3}+\frac{7 i}{3},2+3 i\right\}$. +Answer: +$20+17 i$ \ No newline at end of file diff --git a/pretraining/mathematica/number_theory/lcm/9599.txt b/pretraining/mathematica/number_theory/lcm/9599.txt new file mode 100644 index 0000000000000000000000000000000000000000..57ec04c396267ded2a1a7869817b4cf25628bf6f --- /dev/null +++ b/pretraining/mathematica/number_theory/lcm/9599.txt @@ -0,0 +1,4 @@ +Problem: +Find the least common multiple of $\left\{-\frac{11}{5}+3 i,\frac{5 i}{2},-1\right\}$. +Answer: +$75+55 i$ \ No newline at end of file