Question 44
Determine, with proof, the least positive integer $n$ for which there exist $n$ distinct positive integers $x_{1}, x_{2}, x_{3}, \ldots, x_{n}$ such that
$$
\left(1-\frac{1}{x_{1}}\right)\left(1-\frac{1}{x_{2}}\right)\left(1-\frac{1}{x_{3}}\right) \cdots\left(1-\frac{1}{x_{n}}\right)=\frac{15}{2013}
$$
$$
\left(1-\frac{1}{x_{1}}\right)\left(1-\frac{1}{x_{2}}\right)\left(1-\frac{1}{x_{3}}\right) \cdots\left(1-\frac{1}{x_{n}}\right)=\frac{15}{2013}
$$