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

## Question: 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: [D] 35

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)

Therefore, 4 is the common factor of the HCF 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.

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