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