LCM & HCF Calculator — Least Common Multiple & Highest Common Factor
Calculate the LCM (Least Common Multiple) and HCF (Highest Common Factor) of any numbers online free — also known as LCD and GCD. Shows step-by-step calculation method. No sign-up required.
Last updated: June 2026
Enter up to 6 whole numbers
- LCM (Lowest Common Multiple)
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- HCF (Highest Common Factor)
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About this tool
LCM and HCF, solved and explained
The lowest common multiple (LCM) and highest common factor (HCF) are two of the most useful ideas in number theory, and they appear constantly in school maths — from adding fractions to solving word problems about repeating events. This calculator finds both at once for up to six numbers and, importantly, shows the prime-factorization method behind each answer.
The HCF — also known as the greatest common divisor (GCD) — is the largest number that divides all your inputs without a remainder. The LCM is the smallest number that all of them divide into evenly. They're linked: for two numbers, LCM × HCF equals the product of the numbers. Seeing the prime factors laid out makes the relationship clear and helps you reproduce the method by hand in an exam.
To use it, type your numbers into the boxes — leave the extras blank if you only have two or three — and the LCM, HCF and working update instantly. It's ideal for homework, for simplifying fractions (divide top and bottom by the HCF), and for any situation where you need the smallest shared multiple or largest shared factor. As with every CrispToolHub tool, the calculation happens entirely in your browser and nothing is sent anywhere.
How it works
Three quick steps — no account, nothing uploaded to a server.
Enter your numbers
Type up to six whole numbers into the boxes.
Get both answers
The LCM and HCF appear together instantly.
Follow the steps
See the prime factorization behind each result.
FAQ
Frequently asked questions
What is the difference between LCM and HCF?
The HCF (Highest Common Factor, also called GCD) is the largest number that divides all your numbers evenly — it's about what they share as factors. The LCM (Lowest Common Multiple) is the smallest number that all of them divide into — it's about the smallest common multiple. For 12 and 18, the HCF is 6 and the LCM is 36.
How do I calculate LCM and HCF?
Both come from prime factorization. The HCF is the product of the prime factors common to every number, taken at their lowest powers; the LCM is the product of all prime factors that appear, taken at their highest powers. This calculator does the factorization for you and shows the steps.
When would I use the LCM?
The LCM is used to add or subtract fractions with different denominators (you need a common denominator), to work out when repeating events coincide (two buses leaving at different intervals), and in scheduling and gear-ratio problems. It's the smallest value all the numbers fit into evenly.
When would I use the HCF?
The HCF is used to simplify fractions to lowest terms, to split things into the largest equal groups, and to find the biggest tile or unit that fits two dimensions exactly. It answers 'what is the largest amount these numbers all share?'
Can I find the LCM and HCF of more than two numbers?
Yes — enter up to six numbers and the calculator finds the LCM and HCF of all of them at once by applying the operation pairwise. This is useful for problems involving three or more quantities, which are common in exams.
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