Greatest Common Divisor & Least Common Multiple Calculator

This easy-to-use Greatest Common Divisor (GCD) and Least Common Multiple (LCM) Calculator quickly and easily computes the GCD and LCM for any given set of numbers and generates an in-depth solution for the purposes of analysis.

To use the calculator, all you need to do is enter the integer numbers separated by a comma (e.g., 12, 24, 36, 68); space (e.g., 12 24 36 68); or line break and then hit the "Calculate GCD & LCM" button to generate the results.

What is the Greatest Common Divisor?

The greatest common divisor, which is also commonly referred to as the highest common factor, greatest common factor, or highest common divisor, is the largest positive integer of a given set of numbers that can divide all the numbers within that set without any remainder. Essentially, it is the largest multiple of the numbers within the set.

The GCD is frequently calculated for two numbers as a means of reducing fractions to their lowest terms. If the GCD of two numbers is 1, they are described as relatively prime or coprime.

What is the Least Common Multiple?

As the name indicates, the least common multiple of a group of integer numbers is the smallest multiple of the numbers within the set. Before subtracting or adding fractions that have different denominators, it can be useful to convert all fractions such that the denominator is the LCM of all the denominators. In this event, the LCM is the lowest common denominator (LCD).

GCD and LCM Calculator

An example of a GCD and LCM Calculation

Let's say you want to calculate the GCD and LCM of two numbers: 12 and 28.

First, determine the prime factorizations of 12 = 2 × 2 × 3 and 28 = 2 × 2 × 7.

The GCD is the string that is present in both sets of factorizations, i.e., 2 × 2 = 8.

The LCM is the greatest power of all exponents; i.e., 2 × 2 × 3 × 7 = 84.

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