+586 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?
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
