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The greatest common divisor of positive integers m and n  and  is 6. The least common multiple of  m  and n is 126. What is the least possible value of m+n?

 Jul 3, 2019
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Find all the divisors of 126:

 

126 = 1 | 2 | 3 | 6 | 7 | 9 | 14 | 18 | 21 | 42 | 63 | 

Since 6 the GCD of two numbers in this list, just check one by one:

Since 6 is a divisor of 18 and 42, it therefore follows that they are the 2 numbers sought.

GCD(18, 42) = 6

LCM(18, 42) = 126

Sum =18 + 42 = 60

 Jul 3, 2019
edited by Guest  Jul 3, 2019

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