Problem - 2392
Find the smallest positive integer $n$ such that $\frac{12!}{n}$ is a square.
Answer
231
We factorize $12!$ as $2^{10}\cdot 3^5\cdot 5^2\cdot 7\cdot 11$. Therefore, the answer is $$3\cdot 7\cdot 11=\boxed{231}$$