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Question Number 19634 by Tinkutara last updated on 13/Aug/17

How many ordered triplets (x, y, z) of  positive integer satisfy lcm(x, y) = 72,  lcm(x, z) = 600 and lcm(y, z) = 900?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{ordered}\:\mathrm{triplets}\:\left({x},\:{y},\:{z}\right)\:\mathrm{of} \\ $$$$\mathrm{positive}\:\mathrm{integer}\:\mathrm{satisfy}\:\mathrm{lcm}\left({x},\:{y}\right)\:=\:\mathrm{72}, \\ $$$$\mathrm{lcm}\left({x},\:{z}\right)\:=\:\mathrm{600}\:\mathrm{and}\:\mathrm{lcm}\left({y},\:{z}\right)\:=\:\mathrm{900}? \\ $$

Answered by Tinkutara last updated on 16/Oct/17

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