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LCM calculator

Put value in the input box to calculate the least common multiples by using our lcm finder/calculator.

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Formula

LCM(a,b) = a*b / GCF

Least Common Multiple calculator is an online tool to calculate the least common multiple of two or more numbers. The LCM calculator makes it convenient to calculate the LCM large numbers as well as many numbers as you want. LCM calculator is also referred to as the least common denominator calculator.


How to use LCM calculator?

To use the least common factor calculator, follow these steps:

  • Enter the values in the given input box.
  • Separate each value by using a comma.
  • Press the Calculate button to get the least common factors of the given values.
  • Use the Reset button to reset values for a new calculation.

This calculator is an LCM finder that efficiently calculates the LCM in a few seconds. If you need to calculate the highest common factor, you can use our HCF Calculator anytime.


What is LCM?

The smallest positive integer, which can be divided into two or more integral at the same time, is considered the lowest common multiple. It is expressed as LCM (x, y). LCM stands for Lowest Common Multiple.


How to find the Least Common Multiple?

There are several ways to calculate the LCM in two or more numbers. We have listed and explained some of the important methods to get the LCM below.

Prime Factorization Method

A more formal way of locating the LCM is the prime factorization method. Primary factoring results of the division into their products of prime numbers. Multiplying each primary number with another gets the least common multiple. For multiplication, common numbers are considered only once.

Example:

Find LCM (15, 18, 21)

Step 1: Write down prime factors of all integers.

15: 3 × 5

18: 2 × 3 × 3

21: 3 × 7

Step 2: Multiply the highest number of primary factors for each integer. A number would be considered one time in multiplication if it occurred two or more times in factoring.

2 × 3 × 3 × 5 × 7 = 630

The LCM would be 630 for the given values.


Prime Factorization using Exponents

LCM can also be determined by using the prime factorization with exponents. Follow the steps below to find LCM using this method:

  • Break each number into prime factors and convert them into exponents.
  • Determine the highest number of exponents in each number's prime factors.
  • To get LCM, multiply the highest numbers of exponents from each number.

Example:

Find LCM (12, 16, 20)

Step 1: Break each number into prime factors and convert them into exponents.

12 = 2 × 2 × 3 = 22 × 31

16 = 2 × 2 × 2 × 2 = 24

20 = 2 × 2 × 5 = 22 × 51

Step 2: Determine the highest number of exponents in each number's prime factors, which are:

24, 31, and 51

Step 3: To get LCM, multiply the highest numbers of exponents from each number.

24 × 31 × 51 = 240

The LCM would be 240 for the given numbers using the prime factorization method with exponents. Let's explore one more method to get the least common multiple.


Brute Force Method

LCM can be calculated by using the Brute Force method. All of the numbers must be written in their multiples until they hit the common multiple.

Example:

Find LCM (20, 30)

Write down the multiples of both integers and find a common multiple.
20: 20, 40, 60, 80, 100, 120
30: 30, 60, 90, 120

120 is the common multiple in both integers. So, the LCM is 120 in this example. You can always use our lowest common denominator calculator if you don't want to waste a lot of time on these hefty calculations.

Lcm Table:

LCM of 6 and 8 24
LCM of 12 and 8  24
LCM of 9 and 12 36
LCM of 10, 12 and 6 60
LCM of 9 and 15 45
LCM of 4 and 10 20
LCM of 15 and 25 75
LCM of 4 and 8 8
LCM of 15 and 6 30
LCM of 4 and 14 28

References: 

  1. What is the Least Common Multiple from mathsisfun.com?
  2. Least common multiple - MATLAB lcm
  3. Factoring - Least Common Multiple (LCM) - math.com
  4. Prime Factorization and the Least Common Multiple, math.libretexts.org