Selection and Training Session

Find the least positive integer $n$ for which there exists a set $\{s_1,\dots ,s_n\}$ consisting of $n$ distinct positive integers such that $$\left(1-\frac{1}{s_1}\right)\left(1-\frac{1}{s_2}\right)\cdots \left(1-\frac{1}{s_n}\right)=\frac{51}{2010}$$ (IMO-2010 Shortlist, Problem N1)