🔗GCF & LCM Calculator
Enter two or more positive integers to find their GCF and LCM using prime factorization.
Enter 2 or more positive integers, e.g. 24, 36, 60
Free GCF & LCM Calculator
This GCF and LCM calculator finds the greatest common factor and least common multiple of two or more numbers using prime factorization. Each number is broken into its prime factors, then the GCF takes the lowest power of each shared prime, and the LCM takes the highest power of every prime that appears in any number.
GCF is useful for simplifying fractions and factoring expressions; LCM is essential for adding fractions with different denominators and scheduling problems involving repeating cycles. The prime factorization table below shows exactly how each result is built.
Free, instant, and runs entirely in your browser — no sign-up required.
About the GCF & LCM Calculator
Features
Any number of integers
Works for two numbers or a whole list.
Prime factorization table
See each number's prime powers side by side.
GCF and LCM together
Both results computed at once, no need to run twice.
Instant, private
Runs entirely in your browser. No data is sent anywhere.
Frequently Asked Questions
What is the GCF?
The greatest common factor (GCF), also called the greatest common divisor (GCD), is the largest number that divides evenly into all the given numbers.
What is the LCM?
The least common multiple (LCM) is the smallest positive number that all the given numbers divide into evenly.
How does prime factorization find the GCF and LCM?
Break each number into its prime factors. The GCF multiplies each shared prime raised to its lowest power across all numbers; the LCM multiplies every prime that appears raised to its highest power.
Can I find the GCF and LCM of more than two numbers?
Yes — this calculator accepts any number of comma-separated integers, not just two.
What if the numbers share no common factors?
Their GCF is 1, meaning they're 'coprime' or 'relatively prime.' Their LCM is simply the product of all the numbers.
Why is GCF useful for fractions?
Dividing a fraction's numerator and denominator by their GCF reduces it to lowest terms — for example, 24/36 simplifies to 2/3 by dividing both by their GCF of 12.
Why is LCM useful for fractions?
The LCM of two denominators is the smallest common denominator you can use to add or subtract fractions without unnecessary simplification afterward.
What's the relationship between GCF and LCM?
For two numbers a and b: GCF(a, b) × LCM(a, b) = a × b. This identity only holds directly for exactly two numbers.
Is there a maximum number size?
This calculator supports positive integers up to 10,000,000 to keep prime factorization fast and reliable in the browser.
Is this calculator free to use?
Yes, completely free with no sign-up, and it runs entirely in your browser.