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LCM & HCF Calculator

Find the LCM and HCF (GCD) of two or more numbers with prime factorisation steps.

About LCM & HCF Calculator

This LCM and HCF calculator online finds the lowest common multiple and highest common factor (also called GCD or GCF) of two or more whole numbers. Type the numbers separated by commas or spaces and it shows the prime factorisation of each one, then works out the HCF from the lowest powers of common primes and the LCM from the highest powers of all primes.

Because the steps are shown, it is an easy way to find LCM and HCF and to understand the method for school exams. It works for any number of values, is free to use and runs entirely in your browser.

How to use LCM & HCF Calculator

  1. Type two or more whole numbers separated by commas or spaces.
  2. See the prime factorisation of each number.
  3. Read the HCF (lowest powers of common primes) and LCM (highest powers of all primes).

Frequently asked questions

What is the relation between LCM and HCF?

For two numbers, LCM × HCF = product of the numbers. For 12 and 18: 36 × 6 = 216 = 12 × 18. This does not hold for three or more numbers.

How is HCF found using prime factors?

Take each prime that appears in every number, with its smallest power, and multiply them.

What is the HCF of co-prime numbers?

Co-prime numbers (like 8 and 15) share no prime factor, so their HCF is 1 and their LCM is their product.

What is HCF and LCM?

HCF is the largest number that divides all the given numbers exactly. LCM is the smallest number that is a multiple of all of them.

What is the easiest way to find LCM and HCF?

Write each number as a product of primes. Multiply the common primes at their lowest powers for HCF, and all primes at their highest powers for LCM.

Is LCM always a multiple of HCF?

Yes. The HCF divides every number, and every number divides the LCM, so the LCM is always a multiple of the HCF.

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