2000 Fermat Problem 20

Given a+2b+3c+4d+5e=k and 5a=4b=3c=2d=e, find the smallest positive integer value for k so that a, b, c, d, and e are all positive integers.

\textbf{(A)}\ 87\quad \textbf{(B)}\ 522\quad \textbf{(C)}\ 10\quad \textbf{(D)}\ 120\quad \textbf{(E)}\ 60

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