If p is a positive integer and p^2 is divisible by 12, then the largest positive integer that must divide p ^3 is	Select:
A) 2^3
B) 2^6
C) 3^3
D) 6^3
E) 12^2
Since p is an integer so p cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making p^2 as a multiple of 12))   p^2 is divisible by 12 (12 = 2*2*3), So, p should have at least one 2 and one 3 so that p^2 has a 2^2 and two 3   So, p will have a 2 and a 3. Or p will be a multiple of 6   So, largest possible integer than should divide p^3 is 6^3   So, Answer will be 6^3
<result>D</result>
If p is a positive integer and p^2 is divisible by 12, then the largest positive integer that must divide p ^3 is