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, ………….
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 Math Problems
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