Least Common Multiple (LCM)

Concept

The abbreviation LCM stands for Least Common Multiple. The least common multiple of a number is the smallest number that is the product of two or more numbers. The least common multiple can be calculated for two or more integers as well as two or more fractions. The least common multiple of two numbers is the lowest possible number that can be divisible by both numbers.

There is more than one method to find the LCM of two or more numbers.
1. Listing Method
2. Division/Prime Factorization Method

Rules

To find the LCM using listing method:
1. List the multiples of the numbers that you have to find the LCM of.
2. Find the first common product that appears in both lists.

To find the LCM using division/prime factorization method:
1. Find the least prime that one or more of the numbers are divisible by.
2. Divide the number or numbers by the primes, from the least prime to the greatest prime, until the numbers are reduced to 1. (If a number is not divisible by the prime, bring it down.)
3. Multiply all the primes that were used in this process. The answer is the LCM.

Example

Find the LCM of 18 and 20.

Solution

Method 1 (Listing Method)
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198,….
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200,…
LCM of 18 and 20 is 180.

Method 2 (Division/Prime Factorization)

The LCM = 2 × 2 × 3 × 3 × 5 = 180