Question 52
For each positive integer $n$, let $s(n)$ be the sum of the digits of $n$. Find the smallest positive integer $k$ such that
$$
s(k) = s(2k) = s(3k) = \dots = s(2011k) = s(2012k).
$$
$$
s(k) = s(2k) = s(3k) = \dots = s(2011k) = s(2012k).
$$