LCM and GCD Calculator

The GCD is the largest integer that divides every number in your list without a remainder. The LCM is the smallest positive integer that each of your numbers divides into evenly. They answer opposite questions: the biggest shared factor versus the smallest shared multiple.

It uses Euclid's algorithm. The calculator repeatedly replaces the larger number with the remainder of dividing it by the smaller one until the remainder hits zero, at which point the surviving value is the GCD. For three or more numbers it applies this pairwise across the list.

For any pair the least common multiple equals the absolute value of the product divided by the GCD, so lcm(a, b) = |a times b| / gcd(a, b). The calculator chains this across the whole list to get the overall LCM.

Yes. Enter as many integers as you like separated by commas or spaces. The GCD and LCM are computed by folding the operation over every value, so a list of ten numbers works the same way as a single pair.

The GCD treats zero as a value it divides, so gcd(0, n) is the absolute value of n. Any LCM that involves a zero is defined as zero by convention, and the tool reports zero in that case.

Yes. Signs are ignored for both results because divisibility depends on magnitude, so the GCD and LCM are always reported as non-negative integers.

GCD and LCM are only defined for integers. If you type a decimal or a value that is not a whole number, the tool flags it and asks for an integer instead of guessing.

Yes. Highest common factor (HCF) and greatest common divisor (GCD) are two names for the same thing, which is why the result card is labelled GCD (HCF).

Yes. The calculation runs entirely in your browser with JavaScript, and nothing you type is sent to a server.