2012 Fermat Problem 18

If N is the smallest positive integer whose digits have a product of 1728, then the sum of the digits of N is

\textbf{(A)}\ 28\quad \textbf{(B)}\ 26\quad \textbf{(C)}\ 18\quad \textbf{(D)}\ 27\quad \textbf{(E)}\ 21

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

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