LCM Calculator - Least Common Multiple

By Mateusz Mucha and Hanna Pamuła, PhD candidate
Last updated: Apr 17, 2020

The LCM calculator will determine the least common multiple of two to fifteen numbers for you - no need to fret! This calculation is essential when adding or subtracting fractions with different denominators. The following text will explain what is LCM, show how to find the least common multiple and show how to use the least common multiple calculator.

What is LCM?

The LCM is the least common multiple or lowest common multiple between two or more numbers. We can find the least common multiple by breaking down each number into its prime factors. This can be accomplished by hand or by using the factor calculator or prime factorization calculator. The method for finding the LCM, along with an example illustrating the method, will be seen in the next section.

How to find the Least Common Multiple

Take each number and find its prime factors. Knowing various divisibility rules helps assist in this process.

  1. Any even number is divisible by 2.
  2. Any numbers whose sum of the digits is divisible by 3, is also divisible by 3
  3. A number is divisible by 4 if the last two digits of the number form a number that is divisible by 4
  4. All numbers ending in 5 or 0 are divisible by 5.
  5. The number is divisible by 6 if it is divisible by both 2 and 3.
  6. A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8.
  7. A number whose digits sum to a number divisible by 9 is also divisible by 9.
  8. Any number ending in 0 is divisible by 10.

Once the numbers are broken down to their prime factors, multiply the highest power of each factor to get the LCM.

Least Common Multiple calculator

We are going to show how to find the LCM of 24, 80 and 121. First we'll get the factors of each number. These are: 24 = 2 * 2 * 2 * 3,80 = 2 * 2 * 2 * 2 * 5, 121 = 11 * 11. Gather all the factors, so we have 2, 3, 5, 11. Next multiply the highest power of each of these factors. That gives us 2 * 2 * 2 * 2 * 3 * 5 * 11 * 11 = 29,040. The LCM calculator can be used to check your answer or simply perform this calculation for you.

Just as you need prime factorization to get the LCM, it's equally important to find the GCF, which is the greatest common factor. To find the GCF, take the product of all the common factors of each number. For example, the GCF of 16 and 50 is 2 since the only factor in common between the two numbers is 2. The GCF calculatoris a handy tool to calculate this.

Note that the LCM of two integers is the smallest positive integer the is divisible by both the integers. This is only true if both the integers are not zero. The LCM calculator will display a value of zero in such a case that one or more of the numbers is zero.

Mateusz Mucha and Hanna Pamuła, PhD candidate
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