"Find the smallest positive integral value of $\displaystyle n$ for which the following product is an integer.

$\displaystyle (1\frac{1}{36})$ $\displaystyle (1\frac{1}{37})$ $\displaystyle ...$ $\displaystyle (1\frac{1}{n})$

Justify your answer."

If anybody could give me a hint on how to find this I would appreciate it. Thanks!