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Least common multiple | AMC 8, 2016 - Problem 20

LCM - AMC 8, 2016 - Problem 20


The least common multiple of a and b is 12 .and the lest common multiple of b and c is 15.what is the least possible value of the least common multiple of a and c?

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  • 20

Key Concepts


Algebra

Division algorithm

Integer

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Answer:20

AMC-8, 2016 problem 20

Challenges and Thrills of Pre College Mathematics

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Find greatest common factors

Can you now finish the problem ..........

Find Least common multiple....

can you finish the problem........

we wish to find possible values of a,b and c .By finding the greatest common factor 12 and 15, algebrically ,it's some multiple of b and from looking at the numbers ,we are sure that it is 3.Moving on to a and c ,in order to minimize them,we wish to find the least such that the LCM of a and 3 is 12,$\to 4$.similarly with 3 and c,we obtain 5.the LCM of 4 and 5 is 20 .

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