GCF And LCM Calculator

GCF and LCM Calculator

Find the greatest common factor and least common multiple for two or more positive integers.

Last updated: June 2026 | By Patchworkr Team

Multiple Number Analysis
Number 1
Number 2
Enter positive integers only. The tool calculates the GCF and LCM without silently dropping invalid inputs.
Result
GCF
6
LCM
36
12 x 18 to GCF 6 | LCM 36
GCF x LCM equals the product of the two numbers.

What GCF means

The greatest common factor is the largest positive integer that divides all numbers evenly.

What LCM means

The least common multiple is the smallest positive integer that every number divides.

Formula and example

for two numbers: GCF(a,b) x LCM(a,b) = a x b

Example: 48 and 60 have GCF 12 and LCM 240.

Worked Example

Find GCF and LCM of 48 and 60.

1. Factor 48 = 2^4 x 3.

2. Factor 60 = 2^2 x 3 x 5.

3. GCF = 2^2 x 3 = 12.

4. LCM = 2^4 x 3 x 5 = 240.

Final answer: GCF 12, LCM 240

Frequently Asked Questions

Can I enter more than two numbers?

Yes. The calculator can analyze any length list of positive integers.

Why reject zero and negatives?

GCF and LCM here are defined for positive integers only, so invalid values are rejected explicitly.

Does the relationship always hold?

The simple GCF x LCM = product relationship holds for exactly two numbers.

What if I need the prime-factor method?

You can use the example and the computed values as a check against manual factorization.

Related Tools