GCD & LCM Calculator
Greatest common divisor and least common multiple · free, no signup
Free GCD and LCM Calculator — Greatest Common Divisor & Least Common Multiple
The greatest common divisor (GCD), also called the highest common factor (HCF), is the largest number that divides every number in a set. The least common multiple (LCM) is the smallest number that every number in the set divides into. They are essential for simplifying fractions, finding common denominators and solving scheduling and pattern problems.
Enter two or more whole numbers and this calculator returns both the GCD and the LCM, the prime factorisation of each number, and — for two numbers — the step-by-step Euclidean algorithm so you can follow the working. It handles very large numbers accurately.
Key features
GCD and LCM together
Both results for any list of numbers.
Prime factorisation
See each number broken into primes.
Euclidean steps
Full division steps for two numbers.
Big-number safe
Uses exact integer arithmetic, no rounding errors.
How to use it
- Enter two or more whole numbers separated by commas or spaces.
- Read the GCD and LCM instantly.
- Check the prime factors and Euclidean steps.
- Copy the answer for your homework or project.
Worked example
Example
Numbers: 48 and 180 Prime factors: 48 = 2⁴ × 3, 180 = 2² × 3² × 5 GCD = 12 LCM = 720
Who uses this tool
Students
Learn and check factor and multiple problems.
Teachers
Create worked examples with full steps.
Engineers and planners
Find repeat cycles and common intervals.
Tips for the best results
- Use the GCD to simplify a fraction: divide top and bottom by it.
- Use the LCM to find a common denominator.
- For scheduling, the LCM tells you when repeating events line up again.
- Check with prime factors to understand why the answer works.
Common mistakes to avoid
- Mixing up GCD (smallest shared factor set) with LCM (common multiple).
- Entering decimals; both need whole numbers.
- Forgetting that the GCD of coprime numbers is 1.
Why use AZRS QuickFix?
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Frequently asked questions
Are GCD and HCF the same?
Yes. GCD, GCF and HCF all mean the largest number that divides all the inputs.
How do you find the LCM?
Multiply the numbers and divide by their GCD (for two numbers), or use the highest prime powers.
What is the Euclidean algorithm?
Repeatedly divide and take remainders until the remainder is zero; the last non-zero remainder is the GCD.
Can it handle more than two numbers?
Yes, list as many as you need.
What is the GCD of 0 and a number?
It is that number.
Is this free?
Yes, free and instant in your browser.