GCD / LCM Calculator
Compute GCD and LCM for two numbers.
Greatest common divisor and least common multiple
The GCD — also called the highest common factor — is the largest number that divides both of your numbers cleanly. The LCM is the smallest number both divide into. Together they are the backbone of fraction arithmetic: GCD reduces a fraction to lowest terms, LCM finds the common denominator you need before adding two.
How to use the GCD / LCM Calculator
- Enter Number A.
- Enter Number B.
- Both the GCD and the LCM appear together.
- Use the GCD to simplify a fraction, or the LCM to add two fractions.
Formula and a worked example
GCD by Euclid: gcd(a, b) = gcd(b, a mod b) until the remainder is 0
LCM = (a × b) ÷ gcd(a, b)
Euclid's algorithm is over two thousand years old and still the fastest practical method — it finds the GCD of two large numbers in a handful of steps. Once you have the GCD, the LCM follows from a single division.
Worked example
For 48 and 60: 60 mod 48 = 12, then 48 mod 12 = 0, so the GCD is 12. The LCM is (48 × 60) ÷ 12 = 240. That means 48/60 reduces to 4/5, and any fraction with denominator 48 or 60 can be rewritten over 240.
Frequently asked questions
What is the difference between GCD, HCF and GCF?
Nothing — greatest common divisor, highest common factor and greatest common factor are three names for the same thing.
How do I use the LCM to add fractions?
Find the LCM of the denominators, rewrite both fractions over it, then add the numerators. For 1/4 + 1/6 the LCM is 12, giving 3/12 + 2/12 = 5/12.
What if the two numbers share no factors?
Their GCD is 1 — they are coprime — and the LCM is simply their product.
Can I find the GCD of more than two numbers?
Yes, by chaining: gcd(a, b, c) = gcd(gcd(a, b), c). Run the calculator twice.
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