GCD and LCM Calculator
Find the greatest common divisor (GCD, also called HCF) and the least common multiple (LCM) of two to ten whole numbers, with the prime factorisation that shows where both come from. Enter one number to factorise it or check whether it is prime.
Runs in your browser. Your data is not uploaded.How our tools work
Two to ten numbers from 1 to 1,000,000,000,000, separated by commas or spaces. One number is factorised and checked for being prime.
How do I find the GCD and LCM of numbers?
Write each number as a product of primes. The GCD multiplies the primes they share at their lowest power; the LCM multiplies every prime at its highest power. 12 = 2² × 3 and 18 = 2 × 3², so the GCD is 2 × 3 = 6 and the LCM is 2² × 3² = 36.
- Enter two to ten whole numbers, separated by commas or spaces. Enter a single number to factorise it or check whether it is prime.
- Read the greatest common divisor (GCD, also called HCF or GCF) and the least common multiple (LCM).
- Check the prime factorisation of each number, which shows which powers make up the GCD and the LCM.
Formulas & Methods
GCD from prime factors
Example: 24 = 2³ × 3, 36 = 2² × 3², 60 = 2² × 3 × 5: GCD = 2² × 3 = 12
LCM from prime factors
Example: LCM = 2³ × 3² × 5 = 360
Two numbers
Example: 12 × 18 ÷ 6 = 36
Key features
Up to ten numbers
GCD and LCM of a whole list at once, not just a pair.
Prime factorisation
Each number broken into prime powers, so you can see the working rather than only the answer.
Prime check
Enter one number to factorise it and see whether it is prime.
Where GCD and LCM are used
The GCD is the largest number that divides every value with nothing left over: it is what you divide by to put a fraction or a ratio in lowest terms, and the size of the largest square tile that fits a rectangle exactly. The LCM is the smallest number every value divides into: the lowest common denominator for adding fractions, or the first time two schedules repeating every 12 and 18 days coincide again, after 36 days.
Frequently Asked Questions
Are GCD, HCF and GCF the same thing?
Yes. Greatest common divisor (GCD), highest common factor (HCF) and greatest common factor (GCF) are three names for the same number. HCF is common in British and Indian schools, GCF in American ones.
What is the GCD of two prime numbers?
1, unless they are the same prime. Numbers whose GCD is 1 are called coprime, and their LCM is simply their product, for example 7 × 11 = 77.
Is 1 a prime number?
No. A prime has exactly two different divisors, 1 and itself, and 1 has only one. Leaving 1 out keeps every number’s prime factorisation unique.
Last updated: