# The least $$n$$

Number Theory Level 5

Find the least positive integer $$n$$ such that there exists a set $$\{s_{1}, s_{2},...,s_{n} \}$$ of $$n$$ distinct positive inegers such that $\left(1-\dfrac{1}{s_{1}}\right) \left(1-\dfrac{1}{s_{2}}\right)\cdots \left(1-\dfrac{1}{s_{n}}\right)= \dfrac{51}{2010}.$

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