Least Common Multiple Formula
When two or more numbers have the same numbers as their multiples, these multiples are called 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.
What Is the LCM Formula?
The LCM formula can be expressed as,
LCM Formula:
LCM = (a × b)/HCF(a,b)
where,
- a and b = Two terms
- HCF(a, b) = Highest common multiple of a and b
Examples Using 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 given as,
14 = 2 × 7
35 = 5 × 7
Using least common multiple formula,
L.C.M = 2 × 5 × 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 = 2 × 3 × 7
56 = 2 × 2 × 2 × 7
Using least common multiple formula,
L.C.M = 2 × 2 × 2 × 3 × 7
= 168
Answer: L.C.M. of 14 and 35 is 168.