Least Common Multiple (LCM) is a way of finding the smallest common multiple between any two numbers or more. A common multiple is a multiple of two numbers or more. LCM denotes the less common or multiple factors of any two or more given integers.
Various method of finding LCM
Brute Force method
In this method, the multiples of each number are listed until the first common multiple is found.
Example: Calculate the LCM of 16 and 20.
Let us consider
The multiples of 16 = 16, 32, 48, 64, 80,…..
The multiple of 20 = 20, 40, 60, 80,……
The first common multiple for both the numbers is 80.
So LCM of 16 and 20 is 80.
Prime Factorization method
The prime factorization is one of the most common ways of finding LCM.
Example: Calculate the LCM of 30 and 45.
Let us calculate the prime factors of two number
30 = 2 × 3 × 5
45 = 3 × 3 × 5
Multiply each factor the maximum number of times it occurs in either number.
LCM = 2 × 3 × 3 × 5
LCM = 90
In this method, the two numbers are simultaneously divided with prime numbers until the division is even. When there are no more primes that evenly divide into both numbers, multiply the divisors to get the LCM.
- GCF (Greatest Common Factor) method
The method is used only when the GCF of two numbers is given. The formula used to find the LCM is
L.C.M. = a × b/ gcd (a, b)
Example: Calculate the LCM of 15 and 24. GCF given is 3.
LCM (15 × 24) / 3
LCM = 3.