GCF and LCM Calculator

What This Calculator Does

The greatest common factor (GCF) is the biggest number that divides evenly into all of your numbers - the largest piece they share. The least common multiple (LCM) is the smallest number they all divide into.

A quick picture: for 12 and 18, the largest number that fits into both is 6 (the GCF), and the smallest number both fit into is 36 (the LCM). You meet these two ideas all the time - the GCF is how you reduce a fraction to lowest terms, and the LCM is how you find a common denominator to add fractions.

What GCF and LCM Mean

• GCF = the largest number that divides all of them evenly.
• LCM = the smallest number that all of them divide into evenly.

The GCF is useful for simplifying fractions; the LCM is useful for finding a common denominator.

How to Use It

1. Enter the numbers separated by commas.
2. Read the GCF and the LCM.

Worked Examples

Numbers	GCF	LCM
12, 18	6	36
8, 12	4	24
4, 5	1	20
6, 10, 15	1	30

FAQ

How do you find the greatest common factor?

List the factors each number shares and take the largest, or divide using the Euclidean method. For 12 and 18, the largest shared factor is 6.

How do you find the least common multiple?

Use $\text{LCM}(a, b) = a \times b \div \text{GCF}(a, b)$. For 12 and 18: $12 \times 18 \div 6 = 36$.

Is GCF the same as HCF?

Yes. Greatest common factor (GCF) and highest common factor (HCF) are two names for the same thing.

Can I use more than two numbers?

Yes. Enter any list of whole numbers and the tool finds the GCF and LCM of all of them.