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integer properties from readyforGMAT.com

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by 4meonly » Mon Dec 15, 2008 8:57 am
k is a positive integer and 225 and 216 are both divisors of k. If k=2^a * 3^b * 5^c, where a, b and c are positive integers, what is the least possible value of a+b+c?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

OA [spoiler](E) 8[/spoiler]
I got 9 :?:
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Re: integer properties from readyforGMAT.com

by tritrantran » Mon Dec 15, 2008 9:22 am
4meonly wrote:k is a positive integer and 225 and 216 are both divisors of k. If k=2^a * 3^b * 5^c, where a, b and c are positive integers, what is the least possible value of a+b+c?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

OA [spoiler](E) 8[/spoiler]
I got 9 :?:
225 = 15^2 = (3*5)^2 = 3^2*5^2

216 = 6^3 = (2*3)^3 = 2^3*3^3

225 and 216 are both divisors of k

LCM = 2^3*3^3*5^2

k = 2^a*3^b*5^c = 2^3*3^3*5^2

a = 3, b = 3, c = 2

a+b+c = 3+3+2 = 8

E)

I hope this is the right method.
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by 4meonly » Mon Dec 15, 2008 9:25 am
f***, I was wrong with factorisation of 225
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