GCD & LCM Calculator
Find the Greatest Common Divisor and Lowest Common Multiple for a set of numbers. Simply enter your numbers separated by commas.
Greatest Common Divisor (GCD)
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Least Common Multiple (LCM)
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GCD vs. LCM
The Greatest Common Divisor (GCD), also known as HCF, is the largest positive integer that divides each of the numbers without a remainder. It's useful for simplifying fractions. The Least Common Multiple (LCM) is the smallest positive integer that is a multiple of every number in the set. It is essential when adding or subtracting fractions with different denominators.
Frequently Asked Questions
What is the Euclidean Algorithm? +
This tool uses the Euclidean Algorithm to find the GCD. It works by repeatedly replacing the larger number with the remainder of the larger divided by the smaller until the remainder is zero.
How do you find LCM from GCD? +
For two numbers $a$ and $b$, the relationship is: $LCM(a, b) = (|a \times b|) / GCD(a, b)$. This tool scales that logic to handle multiple numbers efficiently.
Can I calculate for more than two numbers? +
Yes! You can enter as many numbers as you like (e.g., 8, 12, 16, 20). The tool will find the common divisor and multiple that applies to the entire set.
Why is my GCD "1"? +
If the GCD is 1, it means the numbers are "Co-prime." They share no common factors other than 1.
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