2010 AMC 10A Problem 21

The polynomial x^3 -ax^2 + bx -2010 has three positive integer roots. What is the smallest possible value of a?

\mathrm{(A)}\ 78 \qquad \mathrm{(B)}\ 88 \qquad \mathrm{(C)}\ 98 \qquad \mathrm{(D)}\ 108 \qquad \mathrm{(E)}\ 118

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.