AIME 2010a Problem 14

For each positive integer $n$, let $f(n) = \sum_{k = 1}^{100} \lfloor \log_{10} (kn) \rfloor$. Find the largest value of $n$ for which $f(n) \le 300$. Note: $\lfloor x \rfloor$ is the greatest integer less than or equal to $x$.