The LCM of three different numbers is 120. Which of the following cannot be their HCF?

[A] 8

[B] 12

[C] 24

[D] 35

To find the Least Common Multiple (LCM) of two numbers, we need the least number which is exactly divisible by both the numbers without leaving any remainder.

Answer: The LCM of three different numbers is 120, then [D] 35 cannot be their HCF.

LCM is the least common multiple of the given numbers whereas HCF is the highest common factor of those numbers.

Explanation:

LCM is the multiplication of one common factor of the numbers and the other different factors of the numbers.

Write the LCM = 120 into factored form, that is

120 = 2 × 2 × 2 × 3 × 5

= 4(2 × 3 × 5)

⇒ 4 is the common factor of the numbers.

So, the HCF of three numbers is a multiple of 4.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

Since 35 is not the multiple of 4, therefore 35 cannot be their HCF.

Therefore, [D] 35 is the correct option.