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The number of ordered triplet (x, y, z) such that LCM (x, y) = 3375, LCM (y, z) = 1125 and LCM (z, x) = 3375 is

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Best answer

1125 = 53 ⋅32 , 3375 = 53 ⋅33

Clearly, 33 is a factor of x and 32 is a factor of at least one of y and z. This can be done in 5 ways. 

Also, 53 is a factor of at least two of the numbers x, y, z which can be done in (3C2 x 4 – 2) = 10

Number of ordered pair = 10 x 5 = 50.

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