2002 Pascal Problem 21

A rectangular block, with dimensions 4 cm, 5 cm and 6 cm, is made up of cubes each with side length 1 cm. If 1 cm^3 cubes are removed from this larger rectangular block, what is the minimum number of these cubes that must be removed so that the resulting solid is itself a cube?

\textbf{(A)}\ 40\quad \textbf{(B)}\ 93\quad \textbf{(C)}\ 46\quad \textbf{(D)}\ 64\quad \textbf{(E)}\ 56

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.