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GCF and LCM Calculator

Created by Mateusz Mucha and Piotr Małek
Reviewed by Hanna Pamuła, PhD and Jack Bowater
Last updated: Jan 18, 2024


The GCF and LCM calculator (also called the GCF finder) will determine the greatest common factor and least common multiple of a set of two to six numbers. You can also compute the GCF and LCM by hand or use the GCF calculator or the LCM calculator to find more detailed methods to compute these problems by hand.

If you want to find the GCF and LCM, first, you need to get the prime factorization of each number in the set. This is done easily with the prime factorization calculator.

How to use the GCF finder

Suppose you want to find the GCF and LCM of 24 and 56.

  • First we get the prime factorizations of 24 = 2 × 2 × 2 × 3 and 56 = 2 × 2 × 2 × 7.

  • The greatest common factor is what is present in both sets of factors, which is 2 × 2 × 2 = 8.

  • The least common multiple is the highest power of all exponents, which is 2 × 2 × 2 × 3 × 7 = 168.

There are several methods for finding GCF, including prime factorization or the Euclidean algorithm using the modulo calculator. The factor calculator is also a handy tool for finding GCF and LCM. Note that while finding the GCF and LCM of smaller numbers is relatively simple by hand, the GCF and LCM calculator is quicker and much easier for larger or larger sets of numbers.

FAQ

What is the GCF?

The GCF, or greatest common factor, is the highest number that divides exactly two or more numbers. For example, the greatest common factor of 20 and 16 is 4, as both numbers can be divided by that value: 20/4 = 5, 16/4 = 4.

How do I calculate the GCF?

To find the greatest common factor in any set of numbers, follow these easy steps:

  1. Write the prime factorization of the numbers.
  2. Select all the factors shared by the factorizations, with the highest exponent.
  3. Multiply the shared factors.

That's it! The hardest part of this process is finding the prime factors; the rest is straightforward.

What is the GCF of 8, 36, and 12?

The GCF of 8, 36, and 12 is 4. To find it:

  1. Write the prime factors of the three numbers:

    • 8 = 2 × 2 × 2 = 2³;

    • 36 = 2 × 2 × 3 × 3 = 2² × 3³; and

    • 12 = 2 × 2 × 3 = 2² × 3.

  2. Find the factors that repeat in both factorizations. In this case, we have only .

  3. 4 is the greatest common factor as:

    • 8/4 = 2;
    • 36/4 = 9; and
    • 12/4 = 3.

What is the least common multiple?

The least common multiple of a set of numbers is the smallest number greater than each value in the set that is exactly divisible by all numbers in the set. To find the least common multiple, follow these steps:

  1. Write the prime factorizations of the numbers in the set.

  2. Identify all the factors, and chose the highest power in which they appear.

  3. Multiply the factors (and their powers, in case) to find the least common multiple.

Mateusz Mucha and Piotr Małek
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