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# If m and n are positive integer, and 1800m = n3, what is

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If m and n are positive integer, and 1800m = n3, what is [#permalink]  09 Feb 2011, 16:32
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If m and n are positive integer, and $$1800m = n^3$$, what is the least possible value of m?
(A) 2
(B) 3
(C) 15
(D) 30
(E) 45
[Reveal] Spoiler: OA

Last edited by Narenn on 21 Aug 2013, 08:38, edited 1 time in total.
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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]  09 Feb 2011, 16:57
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loveparis wrote:
89. If m and n are positive integer, and 1800m = n3, what is the least possible value of m?
(A) 2
(B) 3
(C) 15
(D) 30
(E) 45

$$1800m=2^3*3^2*5^2*m=n^3$$ the least value of $$m$$ for which $$2^3*3^2*5^2*m$$ is a perfect cube is 3*5=15 (m must complete the powers of 3 and 5 to cubes): in this case $$2^3*3^2*5^2*m=2^3*3^3*5^3=(2*3*5)^3=n^3$$

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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]  09 Feb 2011, 16:55
1800*m=n^3
m=n^3/1800
=n^3/(3^2*5^2*2^3)

so n has to be 3*5*2 so that n^3 is divisible by 1800.

So m= (2*3*5)^3/(3^2*5^2*2^3)
m=15
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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]  18 Jun 2014, 14:31
Hello from the GMAT Club BumpBot!

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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]  18 Jun 2014, 20:04
Hi
This is one of the questions in which plugin the answers will make it much easier.

2.3.15.30.45

1800 *2 = 3600 not a cube
b) 3
5400 not a cube
c) 1800 * 15 = 27000 = 30 to the power of 3

d) and e) are higher, so no need to go ahead further.
ans : C
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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]  29 Jul 2015, 19:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If m and n are positive integer, and 1800m = n3, what is   [#permalink] 29 Jul 2015, 19:46
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