LCM, HCF & Prime Factor Calculator

LCM, HCF and prime factors with factor trees and working.

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LCM, HCF & Prime Factor Calculator

Factor trees, division steps and Euclid's method

NumbersTwo to five whole numbers, separated by commas.

LCM36least common multiple

HCF (GCD)6highest common factor

Prime factors of 122^2 × 3

Prime factors of 182 × 3^2

Factor trees

12 = 2^2 × 3

18 = 2 × 3^2

Division method (LCM)

2	12	18
2	6	9
3	3	9
3	1	3
	1	1

LCM = 2 × 2 × 3 × 3 = 36

How it works

The HCF is the biggest number that divides every number in the list. The LCM is the smallest number that every number divides into. Prime factorisation writes a number as a product of primes, and both come straight from it.

12 = 2 × 2 × 3 = 2^2 × 3.
18 = 2 × 3 × 3 = 2 × 3^2.
HCF: take each prime that appears in every number, with its smallest power: 2 × 3 = 6.
LCM: take every prime that appears, with its largest power: 2^2 × 3^2 = 36.
Check with Euclid's method: 18 = 12 × 1 + 6; 12 = 6 × 2 + 0. The last non-zero remainder is 6.
Check: HCF × LCM = 6 × 36 = 216 = 12 × 18.
Division method for LCM: divide by 2, 2, 3, 3 in turn until every number reaches 1; the product of the divisors is 2 × 2 × 3 × 3 = 36.

For two numbers, HCF × LCM = the product of the numbers.
Coprime numbers have HCF 1, so their LCM is just their product.
Use the LCM to add fractions and the HCF to simplify them.

Trial division by 2 and then odd numbers up to the square root gives the primes. HCF takes the smallest power of each shared prime, LCM the largest power of every prime. Euclid's algorithm and the common-division ladder are shown as checks.

Preparing tool

How to use LCM, HCF & Prime Factor Calculator

Type two to five whole numbers, separated by commas.
Read the LCM, HCF and prime factors, and look at each factor tree.
Follow the working, then copy it or share a link.

Read the detailed guide →

What are the limits of LCM, HCF & Prime Factor Calculator?

Positive whole numbers up to 1,000,000,000,000 only (the LCM must also stay exact, below about 9 quadrillion). Nothing you enter leaves your device.