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