Math Calculators

GCD & LCM Calculator

Find the Greatest Common Divisor and Least Common Multiple for 2 or more comma-separated numbers. Uses the Euclidean algorithm and BigInt for large integer accuracy.

2+ Numbers
Euclidean Algorithm
BigInt Support
Comma-Separated Input
Instant

Numbers

Enter 2 or more integers separated by commas or spaces

GCD

Greatest Common Divisor

LCM

Least Common Multiple

Calculation

GCD(12, 18, 24) = 6
LCM(12, 18, 24) = 72

Every value divides evenly by GCD ✓ Yes

GCD and LCM

The greatest common divisor is the largest positive integer dividing every input. The least common multiple is the smallest positive value divisible by every input.

Euclidean algorithm

For two values, repeatedly replace (a, b) with (b, a mod b) until the remainder is zero. The final non-zero value is the GCD. LCM follows from abs(a × b) / GCD(a, b).

function gcd(a, b) {
  while (b) [a, b] = [b, a % b];
  return Math.abs(a);
}

from math import gcd
lcm = abs(a * b) // gcd(a, b)

Concept	Common use
GCD	Simplifying fractions and grouping
LCM	Repeating schedules and common denominators

Inputs use arbitrary-precision BigInt, so very large integers avoid normal JavaScript number rounding.

Frequently Asked Questions

What is GCD?: GCD (Greatest Common Divisor), also called HCF (Highest Common Factor), is the largest number that divides all given numbers without a remainder. E.g. GCD(12, 18) = 6.
What is LCM?: LCM (Least Common Multiple) is the smallest number that is divisible by all given numbers. E.g. LCM(4, 6) = 12. It is used to add fractions and find common denominators.
What algorithm is used?: GCD is computed using the Euclidean algorithm (gcd(a,b) = gcd(b, a mod b)). LCM is derived as LCM(a,b) = |a×b| / GCD(a,b). Both extend naturally to more than two numbers.
Can I find GCD/LCM of more than 2 numbers?: Yes — enter any count of numbers separated by commas. The GCD and LCM are computed iteratively across all of them.

Disclaimer

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GCD and LCM

The greatest common divisor is the largest positive integer dividing every input. The least common multiple is the smallest positive value divisible by every input.

Euclidean algorithm

For two values, repeatedly replace (a, b) with (b, a mod b) until the remainder is zero. The final non-zero value is the GCD. LCM follows from abs(a × b) / GCD(a, b).

function gcd(a, b) { while (b) [a, b] = [b, a % b]; return Math.abs(a); }

from math import gcd lcm = abs(a * b) // gcd(a, b)

Concept

Common use

GCD

Simplifying fractions and grouping

LCM

Repeating schedules and common denominators

Inputs use arbitrary-precision BigInt, so very large integers avoid normal JavaScript number rounding.

Frequently Asked Questions

What is GCD?

GCD (Greatest Common Divisor), also called HCF (Highest Common Factor), is the largest number that divides all given numbers without a remainder. E.g. GCD(12, 18) = 6.

What is LCM?

LCM (Least Common Multiple) is the smallest number that is divisible by all given numbers. E.g. LCM(4, 6) = 12. It is used to add fractions and find common denominators.

What algorithm is used?

GCD is computed using the Euclidean algorithm (gcd(a,b) = gcd(b, a mod b)). LCM is derived as LCM(a,b) = |a×b| / GCD(a,b). Both extend naturally to more than two numbers.

Can I find GCD/LCM of more than 2 numbers?

Yes — enter any count of numbers separated by commas. The GCD and LCM are computed iteratively across all of them.

Disclaimer

Some tools may use AI, automated processing, third-party services, or server-side processing. Do not rely on these tools as a substitute for professional advice.