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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.

prime factors of 56: 7, 2, 2, 2 prime factors of 840: 7, 2, 2, 2, 3, 5

From Statement 1 m = 56*3 or m=56 Insufficient From Statement 2 m=56; n=840 sufficient

Answer: B _________________

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Product of M & N= LCM *GCD ==>56*840 ==>7^2*2^6*5*3

Stmt 1 m could be 7*2^3*5 or 7*2^3*3.. Stmt 2 Since GCD is 56 both m and n should have 7 *2^3 n =>7 *2^3 *3*5 (n is divisible by 15 so it should have 3 and 5 as a factor).. Sufficient

Re: If the greatest common factor of two integers, m and n, is [#permalink]

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15 Oct 2013, 17:27

It is given GCF = 56 = 7 x 2 x 2 x 2 and LCM = 840 = 56 (GCF) x 15 For more fundamental elaboration:- GCF and LCM ---------- 7 |m , n 2 |m1, n1 2 |m2, n2 2 |m3, n3 --- 1 , 15 or --- 3 , 5 From Statement 1 informs "m" is not divisible by 15, so in above illustration, we can have either 1 or 3 under "m", which makes the statement insufficient to identify the value of m,

From Statement 2 informs "n" is divisible by 15, so in above graphic illustration, we can establish that we will have 1 under "m" and 15 under "n", which is sufficient to derive both the value of n and m

The value of m = 1 x 2 x 2 x 2 x 7 = 56 The value of n = 15 x 2 x 2 x 2 x 7 = 840 m + n = 896

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