Common Multiples

Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers.

Consider the following.

(i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, …………etc.

Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, …………… etc.

Therefore, common multiples of 3 and 4 = 12, 24, ………..etc.

[It can easily be seen that each of the common multiples 12, 24, etc., is exactly divisible by both 3 and 4].

(ii) Multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ………… etc.

Multiples of 5 are: 5, 10, 15, 20, 25, ………… etc.

Therefore, common multiples of 2 and 5 = 10, 20, ………..etc.

[It can easily be seen that each of the common multiples 10, 20, etc., is exactly divisible by both 2 and 5].

(iii) Multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ……etc.

Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, ………… etc.

Multiples of 6 are = 6, 12, 18, 24, …………… etc.

Therefore, common multiples of 2, 3 and 6 = 6, 12, 18, 24, ………..etc.

[It can easily be seen that each of the common multiples 6, 12, 18, 24, etc., is exactly divisible by all three numbers 2, 3 and 6].

Questions and Answers on Common Multiples:

I. Find the common multiple of:

(i) 3 and 4

3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 ………….

4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 ………….

The common multiples of 3 and 4 are 12, 24, 36 ………….

(ii) 2 and 3

2 =

3 =

The common multiples of 2 and 3 are __________

(iii) 4 and 6

4 =

6 =

The common multiples of 4 and 6 are __________

(iv) 5 and 10

5 =

10 =

The common multiples of 5 and 10 are __________

(v) 7 and 8

7 =

8 =

The common multiples of 7 and 8 are __________

Answers:

I. (ii) 6, 12, 18, ……….

(iii) 12, 24, 36, ………..

(iv) 10, 20, 30, …………

(v) 56, 112, ………….

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