k is a positive integer and 225 and 216 are both divisors of k. If k = 2a ×3b ×5c, 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

ankur.agrawal wrote:k is a positive integer and 225 and 216 are both divisors of k. If k = 2a ×3b ×5c, 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) 8 225 = 9*25 216=9*24 LCM of 225 and 216 is 9*25*24 =216*5(5) There should be atleast 5 five multiples. hence answer should be greater than 5. 216 = 2a*3b 36=ab sum of a and b should be minimum. Hence a=b=6 I get a+b+c = 6+6+5 = 17 What am I missing?

I presume that you meant k = 2^a X 3^b X 5^c In that case, LCM of 225,216= 2^3 . 3^3 . 5^2 This will give us the smallest number that will be divisible by both 225 and 216. and hence the smallest value of the sum will be 8. (E)

praveen ..u have nailed it..it has to be 17... U can get 18 if u use a= 4, b=9,c=5 But we are looking for least so u get ur point....

OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT I meant k = 2^a X 3^b X 5^c .

ankur.agrawal wrote:OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT I meant k = 2^a X 3^b X 5^c . Hi Ankur, Excused Request to recheck your psost after/before posting. Because I spent much time thinking what I am doing wrong. We all do mistakes. But just wanted to let you know. Cheers!!

kvcpk wrote:ankur.agrawal wrote:OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT I meant k = 2^a X 3^b X 5^c . Hi Ankur, Excused Request to recheck your psost after/before posting. Because I spent much time thinking what I am doing wrong. We all do mistakes. But just wanted to let you know. Cheers!! I am real sorry. Wont let it happen again.

Why didn't anyone post the answer? Its 7 right? The LCM of both numbers is 5400, which can be broken down into prime numbers: (2^2)x(3^3)x(5^2) and the values of a, b and c are 2, 3 and 2 respectively. 2 + 3 + 2 = 7, so D. 7.

bdevas01 wrote:Why didn't anyone post the answer? Its 7 right? The LCM of both numbers is 5400, which can be broken down into prime numbers: (2^2)x(3^3)x(5^2) and the values of a, b and c are 2, 3 and 2 respectively. 2 + 3 + 2 = 7, so D. 7. 5400 = 2^3*3^3*5^2 answer should be 3+3+2 = 8 HTH!!