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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, ………..
1. 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].
How to find the common multiples of three numbers?
2. Find the two common multiples of 6, 9 and 12.
Solution:
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, …
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, …
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84,….
Thus, 36 and 72 are the two common multiples of 6, 9 and 12.
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
Answer:
A number is said to be a common multiple of two or more numbers, if it is a multiple d each of them.
For example:
The multiples of 2 are 2, 4, 6, 8, 10, 12, 16, … and
The multiples of 4 are 4, 8, 12, 16, 20, 24, …
Since 4, 8, 12, 16, 20, 24, … are the multiples of both 2 and 4, therefore, they are the common multiples of 2 and 4.
Answer:
The least common multiple (LCM) of two or more numbers is the smallest number which a common multiple of all the numbers.
For Example:
Find the LCM of 4 and 6.
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, …
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, …
Common multiples are 12, 24, …
The least common multiple 12.
Hence, the LCM of 4 and 6 is 12.
● Multiples.
Common Multiples.
Least Common Multiple (L.C.M).
To find Least Common Multiple by using Prime Factorization Method.
Examples to find Least Common Multiple by using Prime Factorization Method.
To Find Lowest Common Multiple by using Division Method
Examples to find Least Common Multiple of two numbers by using Division Method
Examples to find Least Common Multiple of three numbers by using Division Method
Relationship between H.C.F. and L.C.M.
Worksheet on H.C.F. and L.C.M.
Word problems on H.C.F. and L.C.M.
Worksheet on word problems on H.C.F. and L.C.M.
5th Grade Numbers Page
5th Grade Math Problems
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