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Omni-MATH / The rightmost nonzero digit in the decimal expansion of 101 ! is the same as the…

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problem

The rightmost nonzero digit in the decimal expansion of 101 ! is the same as the rightmost nonzero digit of nn !, where nn is an integer greater than 101. Find the smallest possible value of nn.
Plain-text mathematical notation (without MathML)
The rightmost nonzero digit in the decimal expansion of 101 ! is the same as the rightmost nonzero digit of n !, where n is an integer greater than 101. Find the smallest possible value of n.
Original LaTeX notation
The rightmost nonzero digit in the decimal expansion of 101 ! is the same as the rightmost nonzero digit of $n$ !, where $n$ is an integer greater than 101. Find the smallest possible value of $n$.

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