The full form of LCM is Least Common Multiple and also noted as Lowest Common Multiple (LCM) or Least Common Divisor (LCD). LCM is the smallest positive integer that is equally divisible by two integers a and b. It is denoted as LCM(a,b). For example, if you take integer a=8 and b=12, the LCM(a,b) i.e., LCM(8,12)=24.
Least Common Multiple Calculator
We have created this handy calculator which is useful for any kind of integers to find out the LCM. Students can get the least common multiple (LCM) of a set of integers with a detailed explanation by using this LCM Calculator. Not only the final result it also displays the solution steps and how it works.
Just give the input numbers that you want to calculate the LCM for two integers. Give the first input in the number1 field and then second input in the number2 field and press on the ‘Calculate LCM’ button which is colored in blue. Make use of spaces or commas to split your numbers, for example, type 5000, 7500. Remember not to use commas within your numbers like 5,000, 7,500.
Finding the Least Common Multiple (LCM)
Our LCM calculator can give the final result of LCM of two numbers in a step by step manner. You can find the Least Common Multiple of two integers in three different methods. They are as follows:
- Using Listing Multiples
- Using Prime Factorization
- Using Greatest Common Factor (GCF) method
How to Find LCM Using Listing Multiples Method
First, take each number that you would like to find the LCM and list out the multiples of each integer separately till one of the multiples arrives on all integer listings.
Find out the least number that has arrived on all of the lists. And finally, that smallest number is the LCM.
Example: Find LCM of two numbers ie., 12 and 18
Multiples of 12: 12, 24, 36
Multiples of 18: 18, 36
Now, our calculator looks for the same number which is the smallest in all the lists and displays it as a result of LCM(12, 18). Here, the similar lowest number will be highlighted in bold and yellow color.
Therefore, LCM of 12 and 18 is 36.
How to Find LCM Using Prime Factorization Method
First and foremost, Find all the prime numbers of each given integer. Now, list out all the prime numbers that you found until most often for anyone given number. Multiply the list of prime factors together to find the LCM.
To find LCM(a,b), first, calculate the prime factorization of both a and b. Implement the same process for the LCM of two given numbers or more than two.
Example: Find LCM of 12 and 18 using prime factorization
Prime factorization of 12 = 2 × 2 × 3
Prime factorization of 18 = 2 × 3 × 3
Using all prime numbers obtained as oftentimes as each occurs most usually we take 2 × 2 × 3 × 3 = 36
Therefore LCM(12,18) = 36.
How to Find Least Common Multiple via Primes using Exponents Method
Steps to be followed for finding LCM of two or more numbers using the prime exponential method:
- First, it performs the prime factors step for each number and write the result in an exponent way.
- Note down all the prime numbers found, utilizing the highest exponent to find the LCM.
Example: LCM(12,18)
Prime Factorization of 12
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 12 are 2, 3. Prime Factorization of 12 in exponential form is: 12 = 22 × 31
Prime Factorization of 18
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 18 are 2, 3. Prime Factorization of 18 in exponential form is: 18 = 21 × 32
Now, multiple the highest exponent prime factors to calculate the LCM of 12 and 18.
LCM(12,18) =22 × 32
Therefore, LCM(12,18) = 36.
How to Find LCM Using GCF Method
In the first step, you should know the formula to calculate the LCM with the Greatest Common Factor (GCF) of two or more numbers. Here, is the formula for finding LCM using GCF:
LCM(a,b) = ( a × b) / GCF(a,b).
Now, calculate the GCF of two numbers and then apply in the above formula to find out the Least Common Multiple of two integers.
Example: Find LCM(12,18)
Find the GCF(12,18) = 6
Use the LCM by GCF formula to calculate the least common multiples of 12, 18:
LCM(12,18) = ( 12 × 18) / 6
LCM(12,18) = 216 / 6
LCM(12,18) = 36
A factor is a number that results when you can equally divide one number by another. In this sense, a factor is also known as a divisor.
The Greatest Common Factor (GCF) of a set of numbers is the largest factor that all the numbers share. The greatest common factor (GCF) is the same as:
- HCF – Highest Common Factor
- GCD – Greatest Common Divisor
- HCD – Highest Common Divisor
- GCM – Greatest Common Measure
- HCM – Highest Common Measure
Other Methods to Find Least Common Divisor (LCD) or LCM
1. Finding LCM Using the Cake Method (Ladder Method)
This cake method utilizes division to calculate the LCM of two or more numbers. Cake and Ladder Method is the easiest and quickest method to find the LCM of a set of numbers. So people use most of this method because it is a simple division.
The cake method is quite similar to some other methods like ladder method, the box method, the factor box method, and the grid method of shortcuts to find the LCM. But the grid and box methods may look some different, but they all do division by primes to get the result of LCM of a set of integers.
2. Finding LCM Using the Division Method
Follow the steps given below and know how to find the Least Common Multiple by using the Division method:
- First, note down the numbers in a row on a white paper or ruled book (your’s wish).
- Start calculating the division by taking the lowest prime number, divide the row of integers by a prime number that is equally divisible by one of your numbers and write down the number in the next row.
- If any of the integers in the row is not divisible by the prime number then write down as it is that number in the next row.
- Go ahead by dividing the rows by prime numbers that divide equally into a minimum one number.
- If the final row of results is filled with all 1’s that means you’re done with the division.
- Now, multiple all the prime numbers from the first column to ending numbers and find the LCM of a set of numbers.
Properties of LCM
- The LCM is associative: LCM(a, b) = LCM(b, a)
- The LCM is commutative: LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c))
- The LCM is distributive: LCM(da, db, dc) = dLCM(a, b, c)
- The LCM is related to the greatest common factor (GCF): LCM(a,b) = a × b / GCF(a,b) and GCF(a,b) = a × b / LCM(a,b)
FAQs on Least Common Multiple LCM of two or more numbers
What is Common Multiple?
The Common Multiples are those numbers that are found in all the lists of each number.
What is the full form of LCM?
LCM stands for Least Common Multiple also referred to as Lowest common multiple(LCM) or Least common Divisor (LCD).
What is the definition of Least Common Multiple(LCM) of numbers?
Least Common Multiple(LCM) of numbers is the smallest number of the common multiples.
What are the different methods to find the LCM of two or more numbers?
There are 5 most common methods that are used by the students and teachers to find out the LCM of numbers. There are as follows:
- Listing multiples,
- Prime factorization,
- Division Method,
- Cake or ladder method, and
- Greatest Common Factor (GCF)
How to Find LCM of a set of numbers using the Prime Exponential Method?
You can get a detailed explanation of how to find the Least Common Multiple(LCM) of two numbers by referring above.