The Greatest Common Divisor (also called HCF — Highest Common Factor) of two or more integers is the largest positive integer that divides each of them without a remainder. For example, GCD(12, 18) = 6.

The Least Common Multiple of two or more integers is the smallest positive integer that is divisible by each of them. For example, LCM(4, 6) = 12.

How are GCD and LCM related?

For any two positive integers a and b, GCD(a, b) × LCM(a, b) = a × b. This relationship is used by this calculator to compute LCM efficiently without overflow.

What is prime factorization?

Prime factorization expresses a number as a product of prime numbers. For example, 60 = 2² × 3 × 5. The GCD uses the minimum exponent of each prime factor; the LCM uses the maximum.

Can this handle very large numbers?

Yes. All arithmetic in this calculator uses JavaScript BigInt, which supports arbitrarily large integers without precision loss.

LCM and GCD Calculator

Name: LCM and GCD Calculator
Availability: InStock
Author: Nham Vu

Enter up to 10 positive integers to instantly find their GCD, LCM, and prime factorizations.

Enter Numbers

Numbers (comma-separated, 2–10 values)

Enter 2–10 positive integers. Decimals and zero are not accepted.

Enter at least 2 numbers on the left to see results.

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Summary

Enter up to 10 positive integers to instantly find their GCD, LCM, and prime factorizations.

How it works

Type your numbers separated by commas in the input field (e.g. 12, 18, 24).
The calculator validates that all entries are positive integers.
Click "Calculate" or press Enter to compute the results.
The GCD and LCM appear as large copyable values on the right.
Scroll down to see prime factorizations and the pairwise GCD table.

Use cases

Simplify fractions by dividing numerator and denominator by their GCD.
Find the least common denominator when adding or subtracting fractions.
Schedule repeating events that align — find when two cycles next coincide.
Verify or check homework answers for number theory problems.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu

LCM and GCD Calculator

Enter Numbers

Prime Factorizations

Pairwise GCD Table