The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number.
Let us find the L.C.M. of 2, 3 and 4.
Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, ...... etc.
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...... etc.
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, ...... etc.
Common multiples of 2, 3 and 4 are 12, 24, 36, ...... etc.
Therefore, the smallest common multiple or least common multiples of 2, 3 and 4 is 12.
Consider the following.
(i) 12 is the least common multiple (L.C.M) of 3 and 4.
(ii) 6 is the least common multiple (L.C.M) of 2, 3 and 6.
(iii) 10 is the least common multiple (L.C.M) of 2 and 5.
We can also find the L.C.M. of given numbers by their complete factorisation.
To find for instance, L.C.M. of 24, 36 and 40, we first factorise them completely.
24 = 2 × 2 × 2 × 3 = 2\(^{3}\) × 3\(^{1}\)
36 = 2 × 2 × 3 × 3 = 2\(^{2}\) × 3\(^{2}\)
40 = 2 × 2 × 2 × 5 = 2\(^{3}\) × 5\(^{1}\)
L.C.M. is the product of highest power of primes present in the factors.
Therefore, L.C.M. of 24, 36 and 40 = 2\(^{3}\) × 3\(^{2}\) × 5\(^{1}\) = 8 × 9 × 5 = 360
Solved examples to find the lowest common multiple or the least common multiple:
Find the L.C.M. of 8, 12, 16, 24 and 36
8 = 2 × 2 × 2 = 2\(^{3}\)
12 = 2 × 2 × 3 = 2\(^{2}\) × 3\(^{1}\)
16 = 2 × 2 × 2 × 2 = 2\(^{4}\)
24 = 2 × 2 × 2 × 3 = 2\(^{3}\) × 3\(^{1}\)
36 = 2 × 2 × 3 × 3 = 2\(^{2}\) × 3\(^{2}\)
Therefore, L.C.M. of 8, 12, 16, 24 and 36 = 2\(^{4}\) × 3\(^{2}\) = 144
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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