LCM = {(2*2*2)*7}
GCF = {(2*2*2) *7} * 3 *5

Theres an (3*5) in the LCM, which could belong to either of the numbers together or one each.

(1) m not divisible by 15, but still could contain either a 3 or a 5. Cant say
(2) n is divisible by 15, so it contains both 3 and 5. So the numbers are 56 and 840. Sufficient

B IMO

Looking for some good explanations!

Good question

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.

IMO E

whts OA?

should be B.

since for 1)
m=56*3,n=56*5
m=56*1,n=56*15
m=56*5,n=56*3 are all possibilities which give different m+n each time.

for B)
m=56*15,n=56*1
is the only possibility

user123321

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.