Smallest Excluded LCM

You are given an array $A$ containing $N$ integers. Find the **smallest** integer $x$ that doesn't occur as the LCM of some [subsequence](https://en.wikipedia.org/wiki/Subsequence) of $A$. The LCM (lowest common multiple) of a set of integers is the smallest positive integer that is a multiple of them all. For example, $\text{LCM}(2, 3) = 6, \text{LCM}(4, 5, 8, 1) = 40, \text{LCM}(13) = 13$.