Given an array of integers, we would like to find their least common multiple $($lcm$).$ For example, the lcm of $\{14,12\}$ is $84,$ lcm of $\{21,5,18\}$ is $630,$ and lcm of $\{15,24,6,12\}$ is $120.$

Design an algorithm named lcm that inputs an integer array and returns the least common multiple of the array's contents.

What is the worst case complexity of your algorithm? Explain.