Are GCD and GCF the same?

For positive integers, yes. GCD means greatest common divisor, while GCF means greatest common factor.

How do you find LCM from GCD?

For two nonzero integers, divide one number by the GCD and multiply by the other number: lcm(a,b) = |a / gcd(a,b) * b|.

Can I enter more than two numbers?

Yes. This calculator supports two to six nonzero integers and combines them pair by pair.

What happens with negative numbers?

The calculator uses absolute values, so the GCD and LCM match the corresponding positive inputs.

GCD and LCM Calculator

Find the greatest common divisor and least common multiple for two to six nonzero integers, with Euclidean algorithm steps and prime factorization.

Nonzero integers

GCD and LCM with steps

English search intent for this page combines GCD, GCF, HCF, and LCM terminology. Users usually want both answers, a quick check, and enough steps to understand the Euclidean algorithm and prime-factor method.

g cd (a, b) \cdot lcm (a, b) = ∣ a \cdot b ∣

For two nonzero integers, GCD and LCM are tied through the product of the two numbers.

Enter two to six nonzero integers.
Use the Euclidean algorithm steps to verify the GCD.
Use prime factorization to see why the LCM includes the highest exponent of each prime.

GCD, GCF, HCF, and LCM terminology

Term	Meaning
GCD	Greatest common divisor
GCF	Greatest common factor, the same idea as GCD for positive integers
HCF	Highest common factor, common in UK-style wording
LCM	Least common multiple

For more than two numbers, the calculator combines values pair by pair from left to right.

Frequently Asked Questions

Sources and References

Calculations are based on the listed reference sources. Links open in a new tab.

Updated: June 2, 2026

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