AMC 12 2000 Problem 4

The Fibonacci sequence $1,1,2,3,5,8,13,21,\ldots$ starts with two $1$'s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?

\textbf{(A)}\ 0 \textbf{(B)}\ 4 \textbf{(C)}\ 6 \textbf{(D)}\ 7 \textbf{(E)}\ 9