LCM and HCF calculator
Enter two or more whole numbers. The page factors each one and builds the LCM and the HCF from those primes.
- Prime factors shown
- Free, no sign-up
Separate whole numbers with commas or spaces. HCF is the highest common factor, also called the GCF or GCD.
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How to use it
- Enter whole numbers separated by commas or spaces.
- Read the prime factorisation of each number.
- The HCF uses the lowest shared powers, and the LCM uses the highest powers.
How the primes become the answers
Each number is written as a product of primes. The highest common factor, also called the greatest common factor (GCF) or greatest common divisor (GCD), keeps a prime only when it appears in every number, and then only to the lowest power. The lowest common multiple keeps every prime that appears anywhere, to the highest power. Multiplying those powers gives the two results.
For 12 and 18 the factors are 2² × 3 and 2 × 3². The HCF is 2 × 3 = 6 and the LCM is 2² × 3² = 36. Negative signs are set aside before the factorisation, because the prime factors belong to the positive value. A list that includes 0 has LCM 0.
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Questions
What is the LCM of 12 and 18?
36. The factor work is 12 = 2² × 3 and 18 = 2 × 3², and the highest powers multiply to 36.
Is HCF the same as GCF?
Yes. HCF, GCF and GCD are three names for the same number. This page uses HCF in the result and shows the shared primes.
Can I enter more than two numbers?
Yes. Every number contributes its primes. The HCF still takes the lowest power found in all of them, and the LCM takes the highest.
What about 1?
1 has no prime factors. It leaves the LCM unchanged and pulls the HCF down to 1 when it is in the list.