Pre-Algebra · Superchallenge problem

What is the smallest positive integer $n$ for which all three of $n \times 0.1\overline{6}$, $\ n \times 0.\overline{27}$ and $n \times 0.3\overline{75}$ are integers? (Here $0.3\overline{75} = 0.3757575\ldots$)