Least Common Multiple Formula
When two or more numbers have the same numbers as their multiples, such multiples are called the common multiples. Out of all the common possible multiples the one that is least (smallest) and common for both the numbers, is said to be their least common multiple LCM. LCM Formula helps in calculating this least common multiple for numbers.
In other words, LCM for some integers, say a and b is, the smallest positive integer which is divisible by both a and b.
Let us learn about the LCM formula using solved examples.
What Is the LCM Formula?
The LCM formula can be expressed as:
L.C.M = a × b/HCF(a,b)
where,
a and b = Two terms
HCF(a, b) = Highest common multiple of a and b
Solved examples on Least Common Multiple

Example 1: Find the LCM of 14 and 35.
Solution:
To find: Least common multiple of 14 and 35
Given:
a = 14
b = 35
Prime factorization of 14 and 35 is:
14 = 1 × 2 × 7
35 = 1 × 5 × 7
Highest common factor HCF (14, 35) = 1 × 7 = 7
Using Least Common Multiple Formula,
L.C.M = a × b/HCF(a,b)
= 14 × 35/7
= 70
Answer: L.C.M. of 14 and 35 is 70.

Example 2: Find the LCM of 42 and 56.
Solution:
To find: Least Common Multiple of 42 and 56
Given:
a = 42
b = 56
Prime factorization of 42 and 56:
42 = 1 × 2 × 3 × 7
56 = 1 × 2 × 2 × 2 × 7
Highest common factor HCF (42, 56) = 1 × 2 × 7 = 14
Using Least Common Multiple Formula,
L.C.M = a × b/HCF(a,b)
= 42 × 56/14
= 2352/14
=168
Answer: L.C.M. of 14 and 35 is 168.