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Double LCM

Source: 2021 Fall AMC 12A #8

November 11, 2021
AMCAMC 12AMC 12 Anumber theoryleast common multiple

Problem Statement

Let MM be the least common multiple of all the integers 1010 through 30,30, inclusive. Let NN be the least common multiple of M,M, 32,32, 33,33, 34,34, 35,35, 36,36, 37,37, 38,38, 39,39, and 40.40. What is the value of NM?\frac{N}{M}? (<spanclass=′latex−bold′>A</span>) 1(<spanclass=′latex−bold′>B</span>) 2(<spanclass=′latex−bold′>C</span>) 37(<spanclass=′latex−bold′>D</span>) 74(<spanclass=′latex−bold′>E</span>) 2886(<span class='latex-bold'>A</span>)\: 1\qquad(<span class='latex-bold'>B</span>) \: 2\qquad(<span class='latex-bold'>C</span>) \: 37\qquad(<span class='latex-bold'>D</span>) \: 74\qquad(<span class='latex-bold'>E</span>) \: 2886
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