LCM & HCF (GCD) Calculator

Instantly calculate Least Common Multiple (LCM) and Highest Common Factor (HCF/GCD) with our responsive tool. Perfect for students, teachers, and professionals.

Least Common Multiple (LCM)

72

The smallest positive integer that is divisible by both numbers

Highest Common Factor (HCF/GCD)

12

The largest positive integer that divides both numbers without remainder

About LCM and HCF (GCD)

Welcome to our free online LCM and HCF (GCD) Calculator! This tool helps you instantly calculate the Least Common Multiple (LCM) and Highest Common Factor (HCF), also known as Greatest Common Divisor (GCD), of any two numbers.

What is LCM?

The Least Common Multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers. It's particularly useful when adding or subtracting fractions with different denominators.

What is HCF/GCD?

The Highest Common Factor (HCF) or Greatest Common Divisor (GCD) is the largest positive integer that divides both numbers without leaving a remainder. This is essential for simplifying fractions to their lowest terms.

How to Use This Tool

  • Enter two positive integers in the input fields
  • Click "Calculate" or press Enter
  • Instantly view LCM and HCF results
  • Use "Clear" to reset the calculator

This tool is completely free to use with no registration required. All calculations happen in your browser in real-time, ensuring your data remains private.

Applications of LCM and HCF

  • Simplifying fractions and mathematical expressions
  • Solving problems related to ratios and proportions
  • Finding common denominators in fractions
  • Solving problems in number theory and algebra
  • Real-world applications in scheduling, cryptography, and engineering

Frequently Asked Questions

What is the difference between LCM and HCF?

LCM (Least Common Multiple) is the smallest number that is a multiple of two or more numbers, while HCF (Highest Common Factor) is the largest number that divides two or more numbers without leaving a remainder.

Can I calculate LCM and HCF for more than two numbers?

This calculator currently supports two numbers, but the concepts can be extended to more numbers. For multiple numbers, you would iteratively find the LCM or HCF of pairs of numbers.

How does the calculator work?

The calculator uses the Euclidean algorithm for GCD calculation and the relationship LCM(a, b) = (a × b) / GCD(a, b) to compute the LCM. All calculations happen in your browser for maximum privacy.

Is there a limit to the numbers I can enter?

While there's no strict limit, extremely large numbers (above 10^15) may cause performance issues or inaccuracies due to JavaScript's number precision limits. For most educational purposes, the calculator works perfectly.

Is this tool completely free?

Yes, this LCM and HCF calculator is 100% free to use with no hidden costs, registration requirements, or usage limits. We believe in providing accessible educational tools for everyone.