GCD & LCM Calculator

Written byOleh Soloninupdated 5 October 2026

Numbers (comma separated)

Result

GCD6
LCM72
Working
12 = 2² · 3 18 = 2 · 3² 24 = 2³ · 3 GCD = 2 · 3 = 6 — shared factors at their lowest powers LCM = 2³ · 3² = 72 — every factor at its highest power
Numbers3

The largest shared factor and the smallest shared multiple

Find the GCD and LCM of two or more numbers at once. Used for simplifying fractions, scheduling repeats and splitting things evenly.

These two ideas are opposites that travel together. The GCD is the biggest number dividing all of yours; the LCM is the smallest number all of yours divide into.

The GCD is how fractions get simplified. The LCM is how you work out when two repeating events coincide — buses at 12-minute and 18-minute intervals meet every 36 minutes.

How to use

Enter the numbers separated by spaces or commas — more than two is fine.
Read the greatest common divisor, the least common multiple and the factorisation of each number.
Look at the factorisation of each number — the divisor and the multiple both fall out of it.

Both answers come from one factorisation

For 12, 18 and 24 the factorisations are 2²·3, 2·3² and 2³·3. Taking the shared primes at their lowest powers gives the greatest common divisor, 2·3 = 6; taking every prime at its highest power gives the least common multiple, 2³·3² = 72.

That is also why the two are linked: for a pair of numbers, their product equals the divisor times the multiple. 12 × 18 = 216, and 6 × 36 is the same 216.

Worked out with this calculator; a GCD of 1 means the numbers are coprime.
Numbers	Factorisations	GCD	LCM
12 and 18	2²·3 and 2·3²	6	36
12, 18, 24	2²·3, 2·3², 2³·3	6	72
8 and 15	2³ and 3·5	1	120

What this calculator shows

The greatest common divisor of every number you enter
The least common multiple of the same set
Support for more than two numbers at a time

What to keep in mind

Works with positive whole numbers; decimals are truncated.
Numbers whose GCD is 1 are coprime — they share no factor beyond 1.

FAQs

What is the GCD used for in practice?

Simplifying fractions, mostly. To reduce 12/18 you divide both by their GCD of 6, giving 2/3 in one step.

When would I need an LCM?

Any repeating-cycle problem. Adding fractions needs a common denominator, and shift patterns or timetables that repeat every 4 and 6 days realign every 12.

What does coprime mean?

Two numbers share no common factor except 1, so their GCD is 1. 8 and 15 are coprime despite neither being prime.

Is GCD × LCM related to the numbers themselves?

For exactly two numbers, yes: multiply the GCD by the LCM and you get the product of the pair. With three or more it no longer holds.

What are the GCD and LCM of 12, 18 and 24?

6 and 72. From the factorisations 2²·3, 2·3² and 2³·3, the divisor takes shared primes at their lowest powers and the multiple takes all primes at their highest.

Where are they actually used?

The divisor reduces fractions — 18/24 divided by 6 becomes 3/4. The multiple finds common denominators and answers questions about repeating cycles, such as when two schedules coincide again.

Worked example

Three numbers at once

Input: 12, 18, 24

Output: GCD 6 · LCM 72

Note: Six divides all three; 72 is the first number all three divide into. Note the LCM is not simply the product — that would be 5184.

Useful links

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GCD & LCM Calculator

Result

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