2013 Pascal Problem 21

The integer 636\,405 may be written as the product of three 2-digit positive integers. The sum of these three integers is

\textbf{(A)}\ 259\quad \textbf{(B)}\ 132\quad \textbf{(C)}\ 74\quad \textbf{(D)}\ 140\quad \textbf{(E)}\ 192

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.