What is the difference between GCD and LCM?

The GCD (greatest common divisor, also called HCF) is the largest whole number that divides all of your numbers exactly. The LCM (least common multiple) is the smallest whole number that all of them divide into exactly.

Can I enter more than two numbers?

Yes. Enter as many whole numbers as you like, separated by commas or spaces, and the calculator finds the GCD and LCM across all of them.

Is GCD the same as HCF?

Yes. GCD (greatest common divisor), HCF (highest common factor) and GCF (greatest common factor) are different names for the same thing — the largest number that divides all your values exactly.

How is the LCM calculated from the GCD?

For two numbers, LCM(a, b) = |a × b| ÷ GCD(a, b). For more numbers the calculator chains this pairwise, folding each value into the running result.

What if I enter a zero or a negative number?

Zeros are ignored because every number divides into zero, which makes the LCM undefined. Negative numbers are handled by their absolute value, so −12 behaves like 12.

Why is the GCD of two coprime numbers 1?

Two numbers are coprime when they share no common factor other than 1, so their GCD is 1. For example, 8 and 15 are coprime, so GCD = 1 and LCM = 120.

Is anything sent to a server?

No — the calculation runs entirely in your browser using the Euclidean algorithm, and nothing you type is ever uploaded.

GCD & LCM Calculator

This calculator finds the greatest common divisor (GCD) and least common multiple (LCM) of any list of whole numbers. The GCD — also called the highest common factor (HCF) — is the largest number that divides every value exactly; the LCM is the smallest number that every value divides into. Both are essential for simplifying fractions, finding common denominators, and scheduling repeating events.

How it works

The tool reads your input, splits it on commas or spaces, keeps only whole non-zero numbers, then computes both results in one pass:

GCD uses the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the two, until one becomes zero; the other is the GCD. For several numbers it folds them pairwise — GCD(a, b, c) = GCD(GCD(a, b), c).
LCM is derived from the GCD using LCM(a, b) = |a × b| ÷ GCD(a, b), chained across the list.

Negative inputs use their absolute value, and at least two non-zero numbers are required.

Example

Enter 12, 18, 24:

GCD: GCD(12, 18) = 6, then GCD(6, 24) = 6
LCM: LCM(12, 18) = 36, then LCM(36, 24) = 72

So 6 divides all three numbers, and 72 is the smallest number all three divide into.

Numbers	GCD	LCM
12, 18	6	36
12, 18, 24	6	72
8, 15	1	120

Everything runs in your browser, so nothing you enter is uploaded.