LCM of two Numbers

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

## Solved LCM Examples

What is the LCM of 9 and 12?

What is the LCM of 40 and 50?

What is the LCM of 75 and 80?

What is the LCM of 90 and 92?

What is the LCM of 23 and 33?

## Applications of LCM

LCM is used in the following scenarios:

In an event that will be repeating many times.

When analyzing something that will repeat again at the same time.

When purchasing or getting multiple items to have enough.

## What is the difference between LCM and HCF?

LCM (Least Common Multiple) and HCF (Highest Common Factor) are two mathematical concepts used in multiple areas of mathematics. However, they solve different problems. The primary application of Least Common Multiple (LCM) is finding the (LCD) Lowest Common denominator of at least two fractions.

On the other hand, HCF is often used in algebra to simplify polynomial equations. In addition to that, it can be used to find the GCF (Greatest Common Factor) of two or more numbers. GCF is the greatest number that is a factor of each given number.