# Find the First Three Common Multiples of: (a) 6 and 8 (b) 12 and 18

## Question:Find the first three common multiples of:

## (a) 6 and 8 (b) 12 and 18

Common multiples of any two numbers are the multiples that are common to both the given numbers

## Answer: (a) The first three common multiples of 6 and 8 are 24, 48, and 72

## (b) The first three common multiples of 12 and 18 are 36, 72, and 108

Let's evaluate the common multiples of the given numbers

## Explanation:

To find the common multiples of given numbers find the LCM of those numbers

The multiples of LCM will be the common multiples of those numbers.

(a)

Prime Factorization of 6 : 2 × 3

Prime Factorization of 8 : 2 × 2 × 2

LCM(6, 8) = 2 × 2 × 2 × 3 = 24

The first three multiples of 24 are 24, 48, and 72

So, the first three common multiples of 6 and 8 are 24, 48, and 72

(b)

Prime Factorization of 12 : 2 × 2 × 3

Prime Factorization of 18 : 2 × 3 × 3

LCM(12, 18) = 2 × 2 × 3 × 3 = 36

The first three multiples of 36 are 36, 72, and 108

So, the first three common multiples of 12 and 18 are 36, 72, and 108

### Thus, (a) The first three common multiples of 6 and 8 are 24, 48, and 72 (b) The first three common multiples of 12 and 18 are 36, 72, and 108

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