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# If n is a multiple 18 and m is a multiple of 30, is mn a multiple of 1

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Senior Manager
Joined: 16 Oct 2020
Posts: 262
Own Kudos [?]: 167 [1]
Given Kudos: 2383
GMAT 1: 460 Q28 V26
GMAT 2: 550 Q39 V27
GMAT 3: 610 Q39 V35
GMAT 4: 650 Q42 V38
GMAT 5: 720 Q48 V41
Re: If n is a multiple 18 and m is a multiple of 30, is mn a multiple of 1 [#permalink]
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avigutman gmatophobia

I used prime boxing to solve this question - could you validate my approach please?

According to the question stem:

n = multiple of 18 = 2 x 3^2 x some integer

m = multiple of 30 = 2 x 3 x 5 x some integer

From this info, we know that mn = 2^2 x 3^3 x 5 x some integer. But because 120 = 2^3 x 3 x 5, we need to find out if the additional multiple of 2 hiding within "some integer" of m or n.

S1. n = 2 x 3 x some integer
Redundant. We already know that n contains 2 x 3^2 at the very least.
INSUFFICIENT.

S2. m = 2^2 x 3 x some integer
This tells us that m does indeed contain the additional multiple of 2 that we need to make mn a multiple of 120.
SUFFICIENT.
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