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Subject – Mathematics
Chapter 3 – FACTORS AND MULTIPLES
Sub-topic-6:- LCM(Lowest Common Multiple)

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.
LCM can be calculated by the following methods:
a. Factorisation Method
b. Prime Factorisation Method
c. Common Division Method

LCM by Factorisation Method
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.

LCM by Prime Factorisation Method
Step I: Resolve each given number into its prime factors and express the factors obtained in
exponent form.

Step I: Find the product of the highest powers of all the factors that occur in any of the given
numbers.

Step III: The product obtained in Step II is the required least common multiple (L.C.M).
For example:
1. Find the least common multiple (L.C.M) of 9 and 15 by using prime factorization method.
Solution:
Step I:
Resolving each given number into its prime factors.
9 = 3 × 3.
15 = 3 × 5.

Step II: The product of all the factors with highest powers.

= 3 × 3 × 5 = 45.

Step III: The required least common multiple (L.C.M) of 9 and 15 = 45.

2. What is the least common multiple (L.C.M) of 16 and 28 by using prime factorization
method?