🔗 GCF and LCM Calculator
Enter two or more whole numbers separated by commas or spaces to get their GCF and LCM.
GCF and LCM
How the GCF and LCM Calculator works
The GCF is found with the Euclidean algorithm. The LCM of two numbers is their product divided by their GCF, repeated across the list.
GCF(a, b): repeat a, b → b, a mod b until b = 0
LCM(a, b) = |a × b| ÷ GCF(a, b)
Step-by-step calculation
- 1Enter whole numbers.
- 2Find the GCF with the Euclidean algorithm.
- 3LCM = product ÷ GCF.
Worked example
For 12, 18 and 30: GCF = 6 and LCM = 180.
GCF and LCM Calculator examples
| Whole numbers | GCF and LCM |
|---|---|
| 8, 12 | GCF 4 · LCM 24 |
| 12, 18, 30 | GCF 6 · LCM 180 |
| 15, 25 | GCF 5 · LCM 75 |
| 6, 21 | GCF 3 · LCM 42 |
| 9, 27, 36 | GCF 9 · LCM 108 |
Other inputs kept at the calculator's default values. Results calculated by this calculator.
Why use a GCF and LCM Calculator?
Simplify fractions and find common denominators.
Important factors that can affect your results
- Only whole numbers.
- Zero is excluded.
- Very large LCMs.
Frequently asked questions
Where are these used?
GCF simplifies fractions; LCM finds common denominators and when repeating events line up.
Is GCF the same as GCD and HCF?
Yes — greatest common factor, greatest common divisor and highest common factor are the same thing.
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Last reviewed November 2026 · How we build and check our tools · Report a problem