What is LCM?

The Least Common Multiple (LCM) is also known as the Least Common Divisor (LCD) and Lowest Common Multiple (LCM). Therefore, the LCM of two numbers is the least number possible that is divisible by both numbers. Moreover, it can be calculated by more than two integers or fractions. For example, let’s take two integers a and b; they are denoted by LCM (a, b) is the lowest positive integer divisible by both a and b.

Method to find Least Common Multiple

There are many methods to find the least Lowest Common Multiple of two integers, a and b. Let’s look at the most common ones with common examples;

Prime Factorization Method

Prime factorization is a more systematic way to find the Least Common Multiple of a given integer. The process involves breaking down all the numbers compared to their products of prime numbers. You get the LCM by multiplying the greatest power of each prime number together. Here is an example of how to use the prime factorization method to find LCM;

Step 1: Represent the numbers as prime factors

Step 2: Find the product of all the prime factors and the highest number of times they occur.

Example: Find the LCM of 30 and 40

Prime factorization of 30 is = 2 × 3 × 5

Prime factorization of 40 is = 2 × 2 × 2 × 5

The product of the prime factors excluding repeated common factors is = 2 × 2 × 2 × 3 × 5 = 120

= 120

Brute Force Method

Brute force is the most basic method of finding the Least Common Multiple. It involves listing each multiple of an integer. Here is an example;

Find the LCM of 60 and 80 using the Brute force method

Multiples of 60: 60, 120, 180, 240, 300, 360…

Multiples of 80: 80, 160, 240, 320, 400, 480…

Therefore the LCM of 60 and 80 is = 240

By using Long Division Method

Step 1: Find a prime factor that is a common divisor for the given integers and write it on the left

Step 2: Divide the number with the prime number as long as it’s a factor for the number and write the answer below

Step 3: If the prime number is not a factor then carry it below as it is. Continue the process until 1 is left in the last row

Example: Find the LCM of 4 and 12 using the Long Division method