GCF and LCM Calculator
Enter two to ten whole numbers to find their greatest common factor and least common multiple.
Result
- Least common multiple (LCM)
- 180
- The GCF is also called the greatest common divisor (GCD) or highest common factor (HCF).
How to use GCF and LCM Calculator
- Type two to ten whole numbers, separated by commas or spaces.
- Read the GCF (HCF) and the LCM.
About this tool
The greatest common factor is the largest number that divides every number in the list. The least common multiple is the smallest number that every number in the list divides into.
The GCF is used to simplify fractions, and the LCM to find a common denominator when adding fractions. For two numbers, GCF × LCM equals their product.
How it is calculated
GCF by the Euclidean algorithm: gcd(a, b) = gcd(b, a mod b).
LCM(a, b) = a × b ÷ GCF(a, b).
Worked examples
- 12, 18, 30: GCF 6, LCM 180.
- 4, 6: GCF 2, LCM 12.
Tips for better results
- Use the GCF to simplify a fraction.
- Use the LCM as the common denominator when adding fractions.
Frequently asked questions
Are GCF, HCF and GCD the same?
Yes. They are different names for the greatest common factor.
How do you find the LCM?
Divide the product of two numbers by their GCF. For more numbers, repeat for each one in turn.
Are my numbers saved or sent anywhere?
No. The calculation runs in your browser on your own device. Nothing you type is sent to Paul Digital or any other server.
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Privacy
The calculation runs in your browser on your own device. The numbers you type are not sent to Paul Digital or any other server. Results are estimates from the numbers you enter and are not financial, tax or legal advice.