I really can't check them all!

Logic Level 3

$1 \div 2\div 3 \div 4\div \cdots \div 12 \div 13$

Add any number of parentheses to the expression above such that the resultant number is an integer and is minimized. Submit your answer as this minimum number.

For instance, we could add 1 pair of parentheses like $1 \div(2\div 3 \div \cdots \div13) = \dfrac{13!}4$ , the resultant number of which is an integer but is not necessarily minimized.