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LCM Transitivity

Source: 2016 AMC 8 #20

November 23, 2016
AMC 82016 AMC 8number theoryleast common multiple

Problem Statement

The least common multiple of aa and bb is 1212, and the least common multiple of bb and cc is 1515. What is the least possible value of the least common multiple of aa and cc?
<spanclass=′latex−bold′>(A)</span>20<spanclass=′latex−bold′>(B)</span>30<spanclass=′latex−bold′>(C)</span>60<spanclass=′latex−bold′>(D)</span>120<spanclass=′latex−bold′>(E)</span>180<span class='latex-bold'>(A) </span>20\qquad<span class='latex-bold'>(B) </span>30\qquad<span class='latex-bold'>(C) </span>60\qquad<span class='latex-bold'>(D) </span>120\qquad <span class='latex-bold'>(E) </span>180
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