What is the greatest common divisor?

The largest whole number that divides two or more numbers with no remainder. For 12 and 18 it is 6, since 6 divides both exactly and no larger shared divisor exists.

How do I find the GCD?

Use the Euclidean algorithm. Repeatedly divide the larger number by the smaller and keep the remainder, until the remainder is zero. The last non zero value is the GCD. For 18 and 12 the remainders are 6 then 0, so the GCD is 6.

What is the least common multiple?

The smallest whole number that is a multiple of every number given. For 4 and 6 it is 12, because 12 is the first number both divide exactly, since 4 does not divide 6.

How do I calculate the LCM?

Divide the first number by their GCD, then multiply by the second. For 4 and 6 the GCD is 2, so 4 divided by 2 is 2, and 2 times 6 is 12. Dividing before multiplying avoids a much larger intermediate number.

What is the relationship between GCD and LCM?

Their product always equals the product of the original numbers. For 12 and 18, the GCD of 6 and the LCM of 36 multiply to 216, which is 12 times 18. This makes an excellent check on any answer.

What does relatively prime mean?

Two numbers are relatively prime when their GCD is 1, meaning the only number dividing both is 1. Distinct prime numbers are always relatively prime, which is why 8 and 15 share no factor beyond 1.

Can I use more than two numbers?

Yes. Enter as many as you like and they are folded together one at a time. The GCD of 48, 18 and 30 is 6, found by taking the GCD of 48 and 18 first and then combining that with 30.

What happens if a zero is included?

The GCD becomes the other numbers unchanged, since every number divides zero, and the LCM becomes zero, since zero is a multiple of every number. This is a valid result rather than an error.

How is a fraction reduced to lowest terms?

Divide the numerator and denominator by their GCD. For 18 over 24 the GCD is 6, and 18 divided by 6 is 3 while 24 divided by 6 is 4, giving 3 over 4, which cannot be reduced further.

Why does the LCM sometimes come back as too large?

Because the result exceeds the largest integer JavaScript represents exactly, which is over 9 quadrillion. Rather than return a number with digits quietly rounded off, this calculator says so, since a plausible but wrong large number is worse than an honest limit.

How to Use the GCD and LCM Calculator

Enter any number of whole numbers and get the greatest common divisor, the least common multiple, the prime factorisation of each, and whether the first two are relatively prime.

Step-by-Step Instructions

1 Enter two or more whole numbers separated by commas, spaces or new lines. Pasting a column from a spreadsheet works directly.
2 Read the GCD and the LCM together. Check them with the identity shown: multiplying the two must equal the product of your inputs.
3 Look at the prime factorisation of each number if you entered more than two, since the pattern usually makes the answer obvious.
4 For fractions, the GCD of the numerator and denominator is the number to divide both by to reduce the fraction.
5 With a single number entered, the result shows its prime factorisation and the full list of its divisors instead.

Understanding the Inputs

Numbers

Two or more whole numbers. Decimal entries and blanks are ignored rather than treated as zero, so a stray character cannot silently change your answer.

How to find it: Pairs of measurements for a shared tile size, repeating event intervals for a shared schedule, the numerator and denominator of a fraction to reduce, or a list of measurements to divide down together.

Why it matters: The GCD and LCM of a list are built by folding the values together one at a time, which is why any number of values gives a meaningful answer rather than needing a separate function per count.

Type: text · Default: 12, 18

Tips & Best Practices

✓ Check your work by confirming GCD times LCM equals the product of your inputs.
✓ Divide before multiplying when computing the LCM by hand, which keeps the intermediate number small.
✓ Use the GCD to reduce a fraction: divide top and bottom by it.
✓ Factorise large numbers, then take the minimum power for the GCD and the maximum for the LCM.

Try the GCD and LCM Calculator

by CalculatorPro Tools · Updated 10-12-2026