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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]

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09 Feb 2011, 17:32
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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, 09:38, edited 1 time in total.
Minor Edit
Manager
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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]

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09 Feb 2011, 17:55
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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]

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09 Feb 2011, 17:57
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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]

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18 Jun 2014, 15:31
Hello from the GMAT Club BumpBot!

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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]

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18 Jun 2014, 21:04
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]

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29 Jul 2015, 20:46
Hello from the GMAT Club BumpBot!

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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]

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16 Mar 2016, 01:39
Here N must contain at-least one 3 and one 5 for m to be an integer
hence C
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Re: If m and n are positive integer, and 1800m = n3, what is [#permalink]

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16 Mar 2016, 02:04
loveparis wrote:
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

1800*m is a cube number'
The first cube number is 27000 when m = 15
Tip: Prime factor 1800:2^3*3^2*5^2; we require one more 3 and one more 5.
Re: If m and n are positive integer, and 1800m = n3, what is   [#permalink] 16 Mar 2016, 02:04
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