LCM and HCF Calculator
Calculate the Lowest Common Multiple (LCM) and Highest Common Factor (HCF/GCD) of two or more numbers instantly. Shows step-by-step working.
About this calculator
The Lowest Common Multiple and Highest Common Factor are core ideas in Indian school maths. Enter two or more numbers and get both, with the prime factorisation of each and the factors that make up the HCF and the LCM.
The step-by-step view helps students see why the answers are what they are.
How to use it
- Enter the numbers separated by commas.
- Press Calculate LCM & HCF.
- Read the HCF, LCM and the prime factorisations.
Prime factorisation method
Factorise each number into primes. The HCF is the product of the primes common to all numbers, each taken to the lowest power. The LCM is the product of all primes that appear, each taken to the highest power. For two numbers, HCF × LCM = product of the numbers.
Worked example
12, 18, 24
| 12 | 2² × 3 |
| 18 | 2 × 3² |
| 24 | 2³ × 3 |
| HCF | 2 × 3 = 6 |
| LCM | 2³ × 3² = 72 |
Tips and common mistakes
- For two numbers, check that HCF × LCM equals their product: 6 × 36 = 216 = 12 × 18.
- The HCF is never larger than the smallest number.
- The LCM is never smaller than the largest.
- Word problems about 'the greatest number that divides' use the HCF.
- Problems about 'the smallest number divisible by' use the LCM.
Frequently asked questions
What is HCF?
The highest common factor, the largest number dividing each given number exactly.
What is LCM?
The lowest common multiple, the smallest number divisible by each given number.
What is the HCF of 12 and 18?
6.
What is the LCM of 12 and 18?
36.
What if the numbers are coprime?
The HCF is 1 and the LCM is their product.
Can I use three or more numbers?
Yes.