The greatest common divisor of positive integers $m$ and $n$ is 8. The least common multiple of $m$ and $n$ is 112. What is the least possible value of $m n$?

Question

Abraham Potter

Mathematics

8 May, 13:44

The greatest common divisor of positive integers $m$ and $n$ is 8. The least common multiple of $m$ and $n$ is 112. What is the least possible value of $m n$?

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Answers (1)

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Johanna Castaneda · Answer 1

8 and 112.

Step-by-step explanation:

as gcd (m, n) = 8 we have that m and n are multiples of 8. Now, as both are multiples of 8 the least common multiple will be the greatest between m and n.

Then, as we need 112 to be the least common multiple m or n has to be 112. Now, the smallest number that is a multiple of 8 is 8. Then, m and n need to be 112 and 8.

gcd (112,8) = 8

lcm (112,8) = 112.

Then, 8 and 112 are the least possible values of m and n.