If the HCF of two numbers is 12, which of the following can never be their LCM?

Question: If the HCF of two numbers is 12, which of the following can never be their LCM?

Solution:
For any two positive integers, the product of their HCF and LCM equals the product of the two numbers:
HCF(a, b) × LCM(a, b) = a × b
This implies that LCM must always be a multiple of the HCF.
Here, HCF = 12, so LCM must be divisible by 12.

Let’s check each option:
a) 36: 36 ÷ 12 = 3 ; Possible
b) 120: 120 ÷ 12 = 10 ; Possible
c) 144: 144 ÷ 12 = 12 ; Possible
d) 90: 90 ÷ 12 = 7.5 ; Impossible

Thus, 90 can never be their LCM when HCF is 12