For a positive integer $n$, define $f(n)$ as the least positive multiple of $n$ that, written in base $10$, uses only digits $\le 2$.

Thus $f(2)=2$, $f(3)=12$, $f(7)=21$, $f(42)=210$, $f(89)=1121222$.

Also, $\sum _{n=1}^{100}{\displaystyle \frac{f(n)}{n}}=11363107$.

Find $\sum _{n=1}^{10000}{\displaystyle \frac{f(n)}{n}}$.