Integer Properties

[sidon]

Hi,
this is an Integer Properties question which I am realy lost with ....

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


Appreciate your help .

Thanks,
sidon

[magizhan]

I guess you got the question wrong. It should have been k = 2^a * 3^b * 5^c in which case

LCM of 225 and 216 is 2^3*3^3*5^2 making the least possible value of a+b+c to be 3+3+2 = 8. Hence E.

[thephoenix]

is the q correct i think its 2^a * 3^b * 5^c
if so then ans is 8

[sidon]

Hi guys ,

Thanks.
You are right I got it wrong should be indeed
k = 2^a * 3^b * 5^c

and the answer is indeed 8 .


Thanks,
Sidon