Exams CBSE LCM Calculator: Online Least Common Multiple Calculator

Written By Tejasvee_S
Last Modified 25-01-2023

LCM Calculator: Online Least Common Multiple Calculator

LCM Calculator is an online tool that helps the person find out the LCM of the given set of numbers within seconds. It can find the LCM of large numbers within seconds. Many different formulas are used to find Least Common Multiple, such as the Prime Factorisation method, division method, greatest common factor method, and other methods which are explained in this article. Here we bring you the information related to the online LCM Calculator and the methods and formulas used to provide an accurate result.

Here we have provided many different methods to calculate LCM. This page is beneficial for students looking for information about LCM, its formulas, and procedures with solved examples. But before proceeding to that, we have given a detailed explanation about multiple, common multiple and LCM. Read all details about LCM Calculator from this page.

What is a Multiple?

Multiple is like a multiplication table. We get a multiple of a number when multiplied by another number, like multiplying any number by 1, 2, 3, 4, 5, and so on, but not with zero (0).

Examples:
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20…
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30…

What is a Common Multiple?

The numbers that have multiple similar numbers of the given numbers.

Examples:
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24…
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30…
Did you notice that 6, 12, 18 and 24 appear in both lists?
So, common multiples of 2 and 3 are: 6, 12, 18, 24, (and 30, 60, 90 and so on)

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What is the LCM?

LCM stands for least common multiple, which mathematically states that it is the lowest common multiple of two (or more) integers a and b, and the smallest positive integer, which gets divisible by both. It is represented as LCM (a, b). So from the previous example, the LCM of 2 & 3 is 6, which is denoted as LCM (2, 3) = 6

How to Find the Least Common Multiple (LCM)?

This LCM calculator finds the LCM by using five different methods:

Listing Multiples
Prime Factorization
Cake/Ladder Method
Division Method
Using the Greatest Common Factor GCF

In the below section, we have explained these steps with examples to understand the complete process easily.

LCM Calculator Using Listing Multiples Method

List down the multiples of each given number separately until at least one similar multiples appears on all list.
Now select the smallest number that is the same on all the lists of multiples
This smallest number is the LCM of all given digits.

Example: LCM (3, 4, 8)
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27…
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32…
Multiples of 8: 8, 16, 24, 32…
Now, Find the smallest number that appears on all of the lists of multiples. In the above numbers, 24 is the smallest number which has a common multiple in all the given numbers. So, LCM (3, 4, 8) is 24.

LCM Calculator Using Prime Factorisation Method

Firstly find all prime factors of each given number.
Now list down all the prime numbers found, as many times as they appear for anyone given number.
Multiply all the numbers list of prime factors together and the LCM is obtained.

Example: find LCM (12,30) using Prime Factorization Method:
Prime factorization of 12 = 2 × 2 × 3
Prime factorization of 30 = 2 × 3 × 5
Now make a group of prime numbers repeating in both numbers and use them one time: 2 × 2 × 3 × 5 = 60. Therefore LCM (12,30) = 60.

LCM Calculator using Prime Factorisation (Exponents)

Take out the prime factors of each number and write them in exponent form.
Make a list of all the prime numbers using the highest exponent found on each number.
Multiply all the prime factors with exponents together to find the LCM.

Example: LCM (12,18, 30)
Prime factors of 12 = 2 × 2 × 3 = 2² × 3¹
Prime factors of 18 = 2 × 3 × 3 = 2¹ × 3²
Prime factors of 30 = 2 × 3 × 5 = 2¹ × 3¹ × 5¹
Make a list of all the prime numbers you found, as many times as they appear most often for anyone given number and multiply them together to find the LCM, So, LCM (12,18, 30) is 2 × 2 × 3 × 3 × 5 = 180
But if you use exponents, you just have to multiply prime numbers with the highest power.
2² × 3² × 5¹ = 180
So LCM (12,18,30) = 180

LCM Calculator Using Cake Method (Ladder Method)

It is a method of division the given numbers to find the LCM. People use the cake or ladder method as it is the simplest, fastest and easiest way to find the LCM by simple division. So to find the LCM

Example: Find the LCM (10, 12, 15, 75)
Write down your numbers in the first layer (row)
Divide the first layer numbers by a prime number which is can divide two or more numbers and bring the result into the next layer.
If any number is not divisible by the selected prime number then just bring down that number as well.
Continue dividing cake layers by prime numbers
Until there no more primes that can be divided into two or more numbers then the division is done.
The LCM is the multiple of all the numbers that come in L shape, left column and bottom row. Number 1 is ignored as multiplying with it result the same number.
LCM = 2 × 3 × 5 × 2 × 5
LCM = 300
Therefore, LCM (10, 12, 15, 75) = 300

LCM Calculator Using the Division Method

In this method, the given numbers are to be divided by prime numbers to find the LCM. Initially, the prime number is selected, which can divide two or more numbers at one go, then moving forward, the numbers to be divided by other prime numbers until the result is one; this is the way to find the LCM by division method. So to find the LCM

Example: Find the LCM(10, 18, 25)
Write the set of numbers in a top row of the table
Now Divide the row of numbers by a prime number which can evenly divide at least one of your numbers and bring the result into the next row of the table.
If any number in the row is not gets divided then just bring down that number in the next tab.
Continue dividing the set of numbers with prime numbers till the result is 1 in the last row of result.
The multiply all the prime numbers used in division.
LCM = 2 × 3 × 3 × 5 × 5 = 450
Therefore, LCM(10, 18, 25) = 450

LCM Calculator Using GCF

This LCM Calculator works on the formula using the Greatest Common Factor GCF of a set of numbers is: The formula is

LCM (a, b) = (a×b)/GCF(a,b)

Example: Find LCM (6,10)
First calculate the GCF (6,10) = 2
Put the details in the formula to calculate: (6×10)/2 = 60/2 = 30
So LCM(6,10) = 30

How to find LCM using Online LCM Calculator?

It is a tool available to find LCM in a few seconds which will help you in saving your time. In this, you just have to fill the set of numbers you need to find LCM and then the result will be displayed. Some LCM calculators use the comma to separate the numbers and some calculators don’t but the details are mentioned so not a thing to worry about. LCM calculators are used to finding LCM of big numbers and if you are a student then we prefer you to follow the manual method to find the LCM as it also helps you in exams. Follow the above methods and you’ll get the LCM easily and then you can verify your result by using LCM Calculators.

FAQs

The frequently asked questions related to LCM Calculator are given below:

Q1. How do you calculate LCM?
A. On this page we have given five different methods to find LCM which are:
1. Listing Multiples
2. Prime Factorization
3. Cake/Ladder Method
4. Division Method
5. Using the Greatest Common Factor GCF

Q2. What is the LCM of 25 and 36?
A. LCM of 25 and 36 is 900.

Q3. What is LCM Calculator?
A. LCM Calculator is an online tool that calculates the LCM of the given set of numbers within seconds.

Q4. What is the LCM method?
A. LCM is the method to calculate the smallest possible multiple of two or more numbers. LCM of two numbers is divisible by both numbers. For example, the LCM of 6 and 8 is 24.

Q5. How do you find the LCM of two numbers?
A. Follow the steps to find the LCM of two numbers:
1. List the first several multiples of each number.
2. Look for multiples common to both lists.
3. Look for the smallest number that is common to both lists.
4. This smallest number is the LCM.

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