P is a positive integer and 225 and 216 are both divisors of P. If P=(2^x)*(3^y)*(5^z), where x, y and z are positive integers, what is the least possible value of x+ y+ z?  Select: A) 4 B) 5 C) 6 D) 8 E) 7
Lets make factorization of 225 and 216 ..   225 = 5 X 5 X 3 X 3 X 3   216 = 2 X 2 X 2 X 3 X 3 X 3   P would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2= 
<gadget id="calculator">3 + 3 + 2</gadget>
<output>8</output>
8(8)(answer) ...
<result>D</result>
P is a positive integer and 225 and 216 are both divisors of P. If P=(2^x)*(3^y)*(5^z), where x, y and z are positive integers, what is the least possible value of x+ y+ z?