🔢 GCD & LCM Calculator
Enter two or more positive whole numbers, separated by commas or spaces, to find their greatest common divisor and least common multiple.
Euclid's algorithm, folded across the list
The GCD of a pair comes from repeated remainders, and the LCM is built from it. Longer lists fold the pair rule left to right:
gcd(a, b) = gcd(b, a mod b) until b = 0
lcm(a, b) = a / gcd(a, b) × bTake the default 24, 36, 60. For 24 and 36: 36 mod 24 = 12, then 24 mod 12 = 0, so the GCD is 12 and the LCM is 24 / 12 × 36 = 72. Fold in 60 and the GCD stays 12 while the LCM becomes 72 / 12 × 60 = 360 - the smallest number all three divide into.
What the inputs accept, and what the answers are for
- Commas or spaces both work. Anything that is not a positive whole number is named in the error, so 2.5 or -8 stops the run rather than being rounded.
- GCD simplifies fractions. 18/24 has a GCD of 6, so it reduces to 3/4.
- LCM gives common denominators and repeat cycles. Jobs running every 24 and 36 days coincide every 72 days.
- Coprime is flagged when the GCD is 1, meaning the numbers share no factor above 1.
Frequently asked questions
What is the GCD of 24 and 36?
12. Both are divisible by 2, again by 2, and by 3, and those factors multiply out to 12.
What is the LCM of 4, 6 and 10?
60. It is the first number 4, 6 and 10 all divide into exactly: 15, 10 and 6 times over.
Does the GCD times the LCM equal the product of the numbers?
Only for exactly two of them: 12 times 72 is 864, and so is 24 times 36. For 24, 36 and 60 the GCD times the LCM is 4,320 while the product is 51,840.