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# If the least common multiple of m and n is 24, then what is

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Intern
Joined: 30 Oct 2017
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If the least common multiple of m and n is 24, then what is [#permalink]  30 May 2018, 01:22
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Question Stats:

71% (01:05) correct 28% (00:33) wrong based on 7 sessions
If the least common multiple of m and n is 24, then what is the first integer larger than 3070 that is divisible by both m and n?

(A) 3072

(B) 3078

(C) 3084

(D) 3088

(E) 3094
[Reveal] Spoiler: OA
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: If the least common multiple of m and n is 24, then what is [#permalink]  05 Jun 2018, 13:10
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Expert's post
Least common multiple of $$m$$ and $$n$$ is 24.

So for a number larger than 3070 to be divisible by both $$m$$ and $$n$$, it must be divisible by the least common multiple of m and n as well.

Using the gre calculator $$\frac{3070}{24}=127.9166$$.

Clearly multiple of 24 larger than 3070 is $$128 \times 24=3072$$.
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Re: If the least common multiple of m and n is 24, then what is [#permalink]  08 Jun 2018, 09:26
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24=23∗324=23∗3

As per divisibility rule -

1. For a number to be divisible by 8, the last 3 digits must be divisible by 8.
2. For a number to be divisible by 3, the sum of the digits must be divisible by 3.

Check the options only (A) follows

1. 072 - Divisible by 8
2. 3072 - Sum of the digits is 12 , which is divisible by 3
Re: If the least common multiple of m and n is 24, then what is   [#permalink] 08 Jun 2018, 09:26
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