Common Multiples
Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers.
A number that is a multiple of two or more numbers is called common multiple those numbers.
For Example:
Let us try to find out the multiples of 8 and 12.
Multiples of 8 are 8, 16, 24, 32, 40, 48............
Multiples of 12 are 12, 24, 36, 48, 60, 72..........
Thus, common multiples of 8 and 12 are 24, 48, ...........
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].
Worksheet 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, ………….
II. Find:
(i) the first two common multiples of 3 and 5.
(ii) the first three common multiples of 5 and 8.
(iii) the first two common multiples of 5 and 10.
(iv) the first five common multiples of 2, 4 and 6.
II. (i) 15, 30
(ii) 40, 80, 120
(iii) 10, 20
(iv) 6, 12, 18, 24, 36
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