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GCD & LCM Calculator

Find the Greatest Common Divisor and Least Common Multiple of any set of numbers.

GCD & LCM Parameters

Enter numbers to find their shared properties.

Example: 12, 18, 30

Method: Prime Factorization

The GCD is the product of common prime factors. The LCM is the product of all prime factors at their highest powers.

Understanding the GCD & LCM Calculator

Find the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) for a set of numbers using prime factorization. Visualize the relationship with a Venn diagram.

Guide

How to use the GCD & LCM Calculator

  • 1Enter a list of numbers separated by commas or spaces (e.g., '12, 18, 30').
  • 2The result cards will instantly show the GCD (HCF) and LCM.
  • 3Examine the 'Factor Intersection' diagram to see the unique and shared prime factors.
  • 4Add more than 2 numbers to calculate multi-number GCD/LCM (Visual diagram supports first 2).
Applications

Common Use Cases

Fractions: Finding specific denominators to add fractions (LCM).
Simplifying: Reducing fractions to lowest terms (GCD).
Scheduling: Finding when two recurring events will align (LCM).
Tiling: Determining max tile size for a rectangular floor (GCD).

The Maths Behind the Calculation

LCM(a,b) = |a × b| / GCD(a,b)

The GCD is the product of the intersection of prime factors (what they share). The LCM is the product of the union of prime factors (all factors needed to build both numbers).

Knowledge Base

Frequently Asked Questions

What is GCD vs HCF?

They are the same thing. Greatest Common Divisor (GCD) and Highest Common Factor (HCF) are interchangeable terms.

Can I calculate GCD for negative numbers?

Typically GCD is defined for positive integers. This calculator treats inputs as positive values.

What if the GCD is 1?

If the GCD is 1, the numbers are 'coprime' or 'relatively prime', meaning they share no common factors other than 1.

Regional Notice: United States

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