AMC 12A 2016 #22

How many ordered triples $(x,y,z)$ of positive integers satisfy $\text{lcm }(x,y) = 72$ , $\text{lcm }(x,z) = 600$ and $\text{lcm }(y,z)=900$ ?

Notation: $\text{lcm }(\cdot)$ denotes the lowest common multiple function.