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What is the least positive integer h for which 120h is equal to the cu

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What is the least positive integer h for which 120h is equal to the cu [#permalink] New post   15 Dec 2021, 02:49
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What is the least positive integer h for which 120h is equal to the cube of an integer?

(A) 120
(B) 180
(C) 225
(D) 240
(E) 300
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C
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Re: What is the least positive integer h for which 120h is equal to the cu [#permalink] New post   15 Dec 2021, 06:44
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We need to find the value of h which will make 120h a perfect cube

Let's start factorizing 120h. We get
120h = \(2^3 * 3 * 5 * h\)
So, for 120h to be a perfect cube
h should be equal to \(3^2 * 5^2\)
Making 120h = \(2^3 * 3 * 5 * 3^2 * 5^2\) = \(2^3 * 3^3 * 5^3\)

=> h = 9*25 = 225

So, Answer will be C
Hope it helps!
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Re: What is the least positive integer h for which 120h is equal to the cu [#permalink]
15 Dec 2021, 06:44
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