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 \(\text{lcm }(y,z)=900\)?

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

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