Given an array of integers, we would like to find their least common multiple

$($

lcm

$)$

$.$

$$For example, the lcm of

$\{$

$1$

$4$

$,$

$1$

$2$

$\}$

$$is

$8$

$4$

$,$

$$lcm of

$\{$

$2$

$1$

$,$

$5$

$,$

$1$

$8$

$\}$

$$is

$6$

$3$

$0$

$,$

$$and lcm of

$\{$

$1$

$5$

$,$

$2$

$4$

$,$

$6$

$,$

$1$

$2$

$\}$

$$is

$1$

$2$

$0$

$.$

$$

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

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