lcm x hcf = product of two numbers
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Question: two numbers have their HCF as 8 and LCM as 1960 .Find the number of such possible pairs.

The factors of 1960 are: 2^3, 5, 7^2   -- note that 2,5,7 are all prime.

Since HCF is 8, then write down the factors as: 8, 5, 7^2

The possible combination of two numbers using these factors, with HCF = 8, is,

(8*1), (8*5*7^2),  i.e. (8), (1960)

(8*5), (8*7^2),      i.e. (40), (392)

(8*7), (8*5*7),      i.e. (56), (280)

There are 3 such pairs: (8, 1969), (40, 392), (56, 280)

by Level 11 User (81.5k points)

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