Least common multiple | 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?

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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