What's the difference between GCF and LCM?

The GCF (greatest common factor, also called GCD) is the largest number that divides evenly into every number in your list — useful for simplifying fractions. The LCM (least common multiple) is the smallest number that every number in your list divides evenly into — useful for finding a common denominator or syncing repeating cycles.

How is the GCF actually calculated here?

Using the Euclidean algorithm, which repeatedly replaces the larger of two numbers with the remainder of dividing it by the smaller, until the remainder hits zero — the last nonzero value is the GCF. It's extended across more than two numbers by applying it pairwise and folding the result into the next number.

Why does the prime factorization matter here?

It's the most intuitive way to see why the GCF and LCM are what they are — the GCF is the product of every prime factor shared across all numbers at its lowest shared power, while the LCM is the product of every prime factor that appears at its highest power across any of the numbers.

Can I use this for more than two numbers?

Yes — enter as many as you like, comma or space separated. The GCF and LCM are both computed across the entire list at once, not just pairwise between the first two.

GCF & LCM CALCULATOR

Find the greatest common factor and least common multiple of two or more numbers, with prime factorizations shown.

Numbers (comma or space separated, 2 or more)

Greatest common factor (GCF)	12
Least common multiple (LCM)	360

Prime factorizations

24	2^3 × 3
36	2^2 × 3^2
60	2^2 × 3 × 5

How to find the GCF and LCM

1
Type two or more positive whole numbers, separated by commas or spaces.
2
The calculator finds the greatest common factor (GCF) and least common multiple (LCM) across all of them at once.
3
Check the prime factorization table to see exactly where each shared factor comes from.

Questions

What's the difference between GCF and LCM?: The GCF (greatest common factor, also called GCD) is the largest number that divides evenly into every number in your list — useful for simplifying fractions. The LCM (least common multiple) is the smallest number that every number in your list divides evenly into — useful for finding a common denominator or syncing repeating cycles.
How is the GCF actually calculated here?: Using the Euclidean algorithm, which repeatedly replaces the larger of two numbers with the remainder of dividing it by the smaller, until the remainder hits zero — the last nonzero value is the GCF. It's extended across more than two numbers by applying it pairwise and folding the result into the next number.
Why does the prime factorization matter here?: It's the most intuitive way to see why the GCF and LCM are what they are — the GCF is the product of every prime factor shared across all numbers at its lowest shared power, while the LCM is the product of every prime factor that appears at its highest power across any of the numbers.
Can I use this for more than two numbers?: Yes — enter as many as you like, comma or space separated. The GCF and LCM are both computed across the entire list at once, not just pairwise between the first two.