If a is a positive integer and a^2 is divisible by 12, then the largest positive integer that must divide a ^3 is  Choose the correct choice
A) 2^3 B) 2^6 C) 3^3 D) 6^3 E) 12^2
Since a is an integer so a 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 a^2 as a multiple of 12))   a^2 is divisible by 12 (12 = 2*2*3), So, a should have at least one 2 and one 3 so that a^2 has a 2^2 and two 3   So, a will have a 2 and a 3. Or a will be a multiple of 6   So, largest possible integer than should divide a^3 is 6^3   So, Answer will be 6^3
<result>D</result>
If a is a positive integer and a^2 is divisible by 12, then the largest positive integer that must divide a ^3 is