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