AMC 10A 2016 Problem 25

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

Answer Choices
A. 15
B. 16
C. 24
D. 27
E. 64