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# What is the smallest positive perfect square that is divisible by 12,

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
What is the smallest positive perfect square that is divisible by 12,  [#permalink]

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29 Apr 2016, 16:04
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Difficulty:

15% (low)

Question Stats:

76% (01:20) correct 24% (01:41) wrong based on 127 sessions

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What is the smallest positive perfect square that is divisible by 12, 15, and 18?

A. 900
B. 1,600
C. 2,500
D. 3,600
E. 4,900

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Joined: 02 Aug 2009
Posts: 7961
Re: What is the smallest positive perfect square that is divisible by 12,  [#permalink]

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30 Apr 2016, 01:14
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Bunuel wrote:
What is the smallest positive perfect square that is divisible by 12, 15, and 18?

A. 900
B. 1,600
C. 2,500
D. 3,600
E. 4,900

HI,
we have to fulfill three conditions..
1) Should be SMALLEST possible
2) Should be a PERFECT square
3) Should be div by 12,15,18..

so it has to be a multiple of LCM of 12,15 and 18..
LCM = >$$12 = 2^2*3$$; $$15 = 3*5$$and $$18 = 2*3^2.$$.
$$LCM = 2*2*3*3*5 = 180$$..
now what should be multiplied to 180 to make it a perfect square=> 180 = 2*2*3*3*5.. ONLY 5 is without pair, so 180 *5 = 900
A
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Re: What is the smallest positive perfect square that is divisible by 12,  [#permalink]

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30 Apr 2016, 02:26
[quote="Bunuel"]What is the smallest positive perfect square that is divisible by 12, 15, and 18?

A. 900
B. 1,600
C. 2,500
D. 3,600
E. 4,900
take the LCM of 12,15,18 that will come 180. the smallest positive perfect square given in the option that can be divided with 180 is 900.
so the ans is (A)
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Re: What is the smallest positive perfect square that is divisible by 12,  [#permalink]

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20 Oct 2018, 22:56
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Re: What is the smallest positive perfect square that is divisible by 12,   [#permalink] 20 Oct 2018, 22:56
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