Difference between revisions of "2005 AMC 10A Problems/Problem 22"
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Revision as of 14:15, 2 August 2006
Problem
Let be the set of the smallest positive multiples of , and let be the set of the smallest positive multiples of . How many elements are common to and .
Solution
Since , the elements that are common to and must be multiples of .
Since and , several multiples of that are in won't be in , but all multiples of that are in will be in . So we just need to find the number of multiples of that are in .
Since every rd element of will be a multiple of
Therefore the answer is