Find the least positive integer $n$ for which there exists a set $\{s_1,s_2,\ldots,s_n\}$ consisting of $n$ distinct positive integers such that
$\left(1-\dfrac{1}{s_1}\right)\left(1-\dfrac{1}{s_2}\right)\dots\left(1-\dfrac{1}{s_n}\right)=\dfrac{51}{2010}.$
Please provide the value of $n$.

Let's think step by step and output the final answer within \boxed{}.
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