GCD / LCM Calculator

Calculate Greatest Common Divisor and Least Common Multiple for any set of numbe...

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Calculator Features

GCD - Greatest Common Divisor
LCM - Least Common Multiple
Steps - Step-by-step solution
Prime Factors - Factorization shown
Multi-Number - Works with many numbers
Factor List - All GCD factors shown

Why Use GCD / LCM Calculator?

GCD & LCM Together

Calculate both Greatest Common Divisor and Least Common Multiple in one place.

Multiple Numbers

Enter any number of values - the calculator works with 2 or more numbers.

Step-by-Step Solution

See how GCD and LCM are calculated iteratively for better understanding.

Prime Factorization

View prime factorization of each number to understand the math.

Copy Results

One-click copy for GCD and LCM values to use elsewhere.

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All calculations happen in your browser. No data sent to servers.

Common Uses

Simplify Fractions

Find GCD to reduce fractions to their simplest form.

Add Fractions

Find LCM to get common denominators when adding fractions.

Math Homework

Verify your work or understand number relationships.

Scheduling

Find when cycles align (like bus schedules or work shifts).

How It Works

1

Enter Your Numbers

Type numbers separated by commas or spaces. For example: 12, 18, 24

2

View GCD Result

See the Greatest Common Divisor - the largest number that divides all inputs evenly.

3

View LCM Result

See the Least Common Multiple - the smallest number divisible by all inputs.

4

Explore Details

Check step-by-step calculations and prime factorizations for deeper understanding.

Math Tips

Coprime Numbers

If GCD is 1, the numbers are coprime (no common factors). LCM will equal their product.

Fraction Simplification

To simplify a fraction, divide both numerator and denominator by their GCD.

Large LCM Values

LCM can grow very large. For numbers with few common factors, LCM approaches their product.

Frequently Asked Questions

GCD is the largest positive integer that divides all the given numbers without leaving a remainder. For example, GCD(12, 18) = 6 because 6 is the largest number that divides both 12 and 18 evenly. GCD is also called HCF (Highest Common Factor).
LCM is the smallest positive integer that is divisible by all the given numbers. For example, LCM(4, 6) = 12 because 12 is the smallest number that both 4 and 6 divide into evenly. LCM is useful for finding common denominators in fractions.
For any two positive integers a and b: GCD(a,b) x LCM(a,b) = a x b. This relationship is used in our calculator for efficient computation. It's a fundamental property in number theory.
Yes! Enter multiple numbers separated by commas, spaces, or newlines. The tool calculates GCD and LCM for all numbers by applying the operations iteratively: GCD(a,b,c) = GCD(GCD(a,b),c) and similarly for LCM.
The calculator uses the Euclidean algorithm for GCD, which is very efficient. For LCM, it uses the relationship: LCM(a,b) = |a x b| / GCD(a,b).
GCD is used to simplify fractions, while LCM is used to find common denominators when adding or subtracting fractions. Both concepts are fundamental in number theory, cryptography, and many areas of mathematics.

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