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.
Use this free online LCM Calculator and provide the input numbers that are given to calculate the LCM of two integers. Give the first input in the number 1 field and then second input in the number 2 field and press on the ‘Calculate’ button which is colored in blue. Remember not to use commas within your numbers like 5,000, 7,500.
Here are some samples of LCM of two numbers calculations.
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.
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 i.e., 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.
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.
Steps to be followed for finding LCM of two or more numbers using the prime exponential method:
Example: Find LCM of 12 and 18 using Primes by Exponents Method
Prime Factorization of 12
Prime factors of 12 are 2, 3. Prime Factorization of 12 in exponential form is: 12 = 22 × 31
Prime Factorization of 18
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.
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:
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.
Follow the steps given below and know how to find the Least Common Multiple by using the Division method:
hcflcm.com is a tool that has different types of calculators for LCM, GCF, HCF, etc. under one roof making it simple for you to solve your problems.
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:
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.