LCM and HCF Calculator

Find the lowest common multiple and highest common factor.

LCM (lowest common multiple)

HCF is 6

HCF / GCD

LCM

Product of all numbers

5184

Coprime

HCF and LCM are computed pairwise across all values.

HCF simplifies fractions and reduces ratios; LCM finds common denominators and answers "when do these cycles coincide".

Prime factorisation of each input, followed by the Euclidean algorithm steps for the first pair.
Number	Prime factorisation
12	2^2 × 3
18	2 × 3^2
24	2^3 × 3
18 = 12 × 1 + 6	remainder 6
12 = 6 × 2 + 0	remainder 0

What does LCM and HCF Calculator do?

Calculate the LCM and HCF (also called GCD) of two or more numbers, with the prime factorisation and Euclidean algorithm steps shown so the method is clear, not just the answer.

How to Use LCM and HCF Calculator

1
Enter your numbersSeparated by commas or spaces.
2
Read both resultsLCM and HCF together.
3
Expand the workingFactorisation and algorithm steps are shown.

Key Features

Two or more numbers at once
Prime factorisation of each input
Euclidean algorithm steps shown for the HCF
Verification that LCM × HCF equals the product, for two numbers
Exact BigInt arithmetic for very large integers

Frequently Asked Questions

What is the difference between LCM and HCF?

HCF is the largest number that divides all of them; LCM is the smallest number they all divide into. For 12 and 18, the HCF is 6 and the LCM is 36.

How does the Euclidean algorithm work?

Repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is zero. The last non-zero value is the HCF. It is over two thousand years old and still the fastest general method.

How do I find the LCM from the HCF?

For two numbers, LCM = (a × b) ÷ HCF. That identity does not extend to three or more, which must be done pairwise or from the prime factorisations.

Where is this actually used?

HCF simplifies fractions and reduces ratios. LCM finds common denominators and answers "when do these two cycles coincide" — buses at 12 and 18 minute intervals meet every 36 minutes.

Runs in your browser

All arithmetic runs in your browser, using exact BigInt maths where whole numbers are involved so nothing is lost to floating-point rounding.

How the rest of the site handles data