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 for a + b + c
a) 4
b) 5
c) 6
d) 7
e) 8
when you break this one down into prime numbers, for 225 you get 5*5*3*3 and for 216 you get 2*2*2*3*3*3. So, it looks like you will need another 2 and 3 to get the perfect square for a grand total of 2 5s, 6 3s, and 4 2s. Since 12 is not an answer, it looks like you can cut out some of those 3s and 2s. Can someone please explain to me the logic?
a) 4
b) 5
c) 6
d) 7
e) 8
when you break this one down into prime numbers, for 225 you get 5*5*3*3 and for 216 you get 2*2*2*3*3*3. So, it looks like you will need another 2 and 3 to get the perfect square for a grand total of 2 5s, 6 3s, and 4 2s. Since 12 is not an answer, it looks like you can cut out some of those 3s and 2s. Can someone please explain to me the logic?
