GmatKiss wrote:If the greatest common factor of two integers, m and n, is 56 and the least common multiple is 840, what is the sum of the m and n?
(1) m is not divisible by 15.
(2) n is divisible by 15.
LCM = (all the prime factors that M and N have IN COMMON) * (all the prime factors that M and N DON'T have in common).
GCF = the product of all the prime factors that M and N have IN COMMON:
56 = 2³ * 7.
Since 840 = 2³ * 3 * 5 * 7, the prime factors that M and N DON'T have in common are 3 and 5.
Thus, 3 must be a factor of M or N (but not both) and 5 must be a factor of M or N (but not both).
To determine M+N, we need to know which of the two (M or N) is a multiple of 3 and which is a multiple of 5.
Statement 1: M is not divisible by 15.
Thus, the following are possible:
M is a multiple of 3 and N is a multiple of 5.
M is a multiple of 5 and N is a multiple of 3.
N is a multiple of both 3 and 5 and M is a multiple of neither.
INSUFFICIENT.
Statement 2: N is divisible by 15.
Thus, N is a multiple of both 3 and 5.
M is a multiple of neither.
SUFFICIENT.
The correct answer is
B.
Statement 2 indicates the following:
N = (all the prime factors that M and N have in common) * (all the prime factors belonging only to N) = 2³ * 7 * 3 * 5 = 840.
M = (all the prime factors that M and N have in common) = 2³ * 7 = 56.
M+N = 840+56 = 896.
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