A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 32 inches. Find b. Choose the correct choice from the following.
A) 8
B) 16
C) 24
D) 32
E) 48
From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x&gt;=2.   From the second premise, we know that the LCM of 12 (2^2*3) andbis 32 (2^5), sob=2^5   Combining 2 premises shows the answer is 32(32).
<result>D</result>
A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 32 inches. Find b.