The HCF of two numbers is 12. Which one of the following can never be their LCM?

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1)
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  1. 72
  2. 60
  3. 90
  4. 84

Answer (Detailed Solution Below)

Option 3 : 90
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Detailed Solution

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Given:

The HCF of two numbers is 12. 

Concept used:

1. If P is the HCF of A and B then, A = P × m and B = P × n.

2. LCM is the smallest common multiple of two or more numbers.

Calculation:

Let the ratio of two numbers be A : B and their HCF be H and LCM be L.

Then, the numbers are AH and BH respectively.

LCM (AH, BH) i.e. L = H × A × B

Hence, L is a multiple of H.

Accordingly, if the HCF of two numbers is 12, then their LCM has to be multiple of 12.

Hence, 90 can't be their LCM.

∴ 90 can never be their LCM.

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