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

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