GCD & LCM Calculator
Find the greatest common divisor and least common multiple of a list of numbers.
Results update as you type.
About this calculator
This calculator finds the greatest common divisor (GCD) — the largest number that divides all your values evenly — and the least common multiple (LCM), the smallest number they all divide into. Enter two or more whole numbers separated by commas or spaces and it also tells you whether they are coprime.
The GCD is found with the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the two until one becomes zero; the other is the GCD. The LCM is then built up pairwise using LCM = a × b ÷ GCD. For 12, 18 and 24 the greatest common divisor is 6 and the least common multiple is 72. When the GCD is 1 the numbers share no common factor and are called coprime.
The GCD is what you use to reduce a fraction to lowest terms, while the LCM gives the common denominator for adding fractions and the period at which repeating cycles line up. The result is the same no matter what order you enter the numbers in.
Frequently asked questions
How is the GCD calculated?
It uses the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the two, until one becomes zero. The other is the GCD.
How are GCD and LCM related?
For two numbers, GCD × LCM = the product of the numbers. So LCM = a × b ÷ GCD, which is how the tool extends the LCM across a whole list.
What does coprime mean?
Two or more numbers are coprime when their greatest common divisor is 1 — they share no common factor other than 1. The tool flags this for you.
Can I enter more than two numbers?
Yes. Separate whole numbers with commas or spaces and the GCD and LCM are computed across the entire list.
What is the GCD and LCM of 12, 18 and 24?
The greatest common divisor is 6 (the largest number dividing all three) and the least common multiple is 72.
Does the order of the numbers matter?
No. Both the GCD and the LCM are the same regardless of the order you type the numbers in.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/gcd-lcm/curl
curl "https://calculator.free/api/v1/gcd-lcm/?numbers=12, 18, 24"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/gcd-lcm/?" + new URLSearchParams({
"numbers": "12, 18, 24"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.