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Out of three numbers A, B, and C, A is the largest number, and the ratio of B to C is 4 : 5. If HCF of A and B is 16, LCM of B and C is 240, and LCM of A and B is 192, then what is the LCM of A, B, and C?

Out of three numbers A, B, and C, A is the largest number, and the ratio of B to C is 4 : 5. If HCF of A and B is 16, LCM of B and C is 240, and LCM of A and B is 192, then what is the LCM of A, B, and C? Correct Answer 960

Given:

HCF of A and B is 16

LCM (B, C) = 240

LCM (A, B) = 192

Calculation:

Let A be 16a and B be 16b

⇒ C = 16b × (5/4) = 20b

LCM of B and C = LCM of ‘16b’ and ‘20b’ = 240

⇒ 80b = 240

⇒ b = 3

B = 16b = 48

C = 20b = 60

LCM of A and B = LCM of ‘16a’ and 48 = 192

⇒ 48a = 192

⇒ a = 4

A = 16a = 64

∴ LCM of A, B and C = LCM of 64, 48, 60 = 960

 

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