# 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.

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