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HQ8T

LCM & HCF Calculator

Find the LCM and HCF of numbers with prime factors.

HCF (GCD)
6
LCM
180

Prime factorisation method

  • 12 = 2² × 3
  • 18 = 2 × 3²
  • 30 = 2 × 3 × 5
  • HCF = lowest power of each common prime = 2 × 3 = 6
  • LCM = highest power of every prime = 2² × 3² × 5 = 180

How to use

  1. 1Type two or more whole numbers separated by commas or spaces.
  2. 2See the HCF and LCM instantly.
  3. 3Read the prime factorisation of each number.
  4. 4Use the steps to check your homework method.

Frequently asked questions

What is the difference between HCF and LCM?

HCF (Highest Common Factor, also called GCD) is the largest number that divides all the numbers. LCM (Lowest Common Multiple) is the smallest number that all of them divide into.

How is HCF found by prime factorisation?

Write each number as a product of primes, then multiply the common primes using their lowest powers. For LCM, multiply every prime using its highest power.

Is HCF × LCM always equal to the product of the numbers?

Only for two numbers. For 12 and 18: HCF 6 × LCM 36 = 216 = 12 × 18. It doesn't hold for three or more numbers.

How many numbers can I enter?

Up to 20 whole numbers above zero.

What is the HCF of co-prime numbers?

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

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