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GCD & LCM Calculator

Finding greatest common factors and least common multiples is essential for simplifying polynomials, working with fractions, and solving modular arithmetic.

Calculated Result
GCD: 12 | LCM: 72

GCD & LCM

Greatest Common Divisor (GCD)

12

Least Common Multiple (LCM)

72

Product (a × b)

864

Calculation Breakdown

  1. Euclidean Algorithm (GCD)Greatest Common Divisor of 24 and 36 is 12\gcd(24, 36) = 12
  2. Least Common Multiple (LCM)LCM = (|a × b|) ÷ GCD = (24 × 36) ÷ 12 = 72\text{lcm}(a, b) = \frac{|a \cdot b|}{\gcd(a, b)} = 72

GCD vs LCM Comparison

Interactive visualization based on your current inputs

Value
0.018365472GCDLCMMetricValue

What Is the GCD & LCM Calculator?

A GCD and LCM Calculator computes common divisors and multiples.

How Does the GCD & LCM Calculator Work?

Uses Euclidean division.

GCD & LCM Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

LCM(a,b)=∣a⋅b∣gcd⁡(a,b)\text{LCM}(a, b) = \frac{|a \cdot b|}{\gcd(a, b)}

Euclidean division algorithm and reciprocal product relationship.

How to Use the GCD & LCM Calculator

  1. Enter two positive integers.

Step-by-Step Example Calculation

GCD and LCM of 24 and 36

Input Values:

a:24
b:36
Worked Steps: GCD is 12; LCM is 72.

Understanding Your Result

Reports both GCD and LCM.

Factors That Affect the Result

  • Prime factorizations.

When Should You Use This Calculator?

  • Number theory and fraction arithmetic.

Assumptions & Limitations

  • Whole integers.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Exact discrete integer operations.

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