LCM & GCD Finder
Enter numbers separated by commas or spaces
LCM & GCD Calculator — Find the Least Common Multiple and Greatest Common Divisor
This LCM and GCD calculator helps you quickly find the greatest common divisor (GCD) and the least common multiple (LCM) for two or more positive integers. Just enter your numbers (separated by commas or spaces) and get accurate results instantly. It’s useful for math homework, exam practice, fraction simplification, and solving problems with repeating cycles.
What Is GCD?
The GCD is the largest number that divides all given numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6, because 6 divides both numbers exactly. GCD is commonly used to simplify fractions and reduce ratios to their simplest form.
What Is LCM?
The LCM is the smallest positive number that all given numbers can divide into evenly. For instance, the LCM of 4 and 6 is 12, because 12 is the smallest number that is a multiple of both 4 and 6. LCM is helpful when you need to combine schedules, add fractions with different denominators, or find when repeating events line up again.
How This Calculator Works
This tool uses the Euclidean Algorithm to compute the GCD efficiently. Once the GCD is known, it uses the relation LCM(a, b) = (a × b) / GCD(a, b) to compute the LCM. For more than two numbers, the calculator applies the same method step by step across the full list.
Examples
- 12, 18, 24 → GCD = 6, LCM = 72
- 8, 14 → GCD = 2, LCM = 56
Frequently Asked Questions
Can I enter more than two numbers?
Yes. This calculator supports multiple numbers at once. Use commas or spaces to separate them.
Why does the tool require positive integers?
GCD and LCM are usually defined for positive integers in most school-level math problems. Using positive values keeps results clear and consistent.
What’s the difference between GCD and LCM?
GCD finds the largest shared divisor, while LCM finds the smallest shared multiple.
