2016 AMC 8
Complete problem set with solutions and individual problem pages
The least common multiple of and is , and the least common multiple of and is . What is the least possible value of the least common multiple of and ?
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Solution 1
We wish to find possible values of , , and . By finding the greatest common factor of and , we can find that is 3. Moving on to and , in order to minimize them, we wish to find the least such that the least common multiple of and is , . Similarly, with and , we obtain . The least common multiple of and is
Solution 2
The factors of are . The factors of are . The numbers that repeat are and so either has to be or . If is then is and is and the least common multiple of and are . We don't have to test because is the lowest answer, so if b equaling resulted in the least common multiple being less that then the correct answer won't be there. So the answer is .
