Euclidean Algorithm Calculator

This Euclidean Algorithm Calculator allows users to find the Greatest Common Divisor (GCD), Least Common Multiple (LCM), Bézout’s Identity Coefficients, and determine if two numbers are coprime.

Use Our Euclidean Algorithm Calculator

Step-by-Step Guide to Using the Euclidean Algorithm Calculator

Introduction

The Euclidean Algorithm Calculator is a useful tool designed to compute the Greatest Common Divisor (GCD), Least Common Multiple (LCM), Bézout’s Identity coefficients, and determine if two numbers are coprime. Follow the steps below to get started with the calculator.

Step 1: Input Your Numbers

  1. Enter the First Number (a): Use the input field labeled ‘First Number (a)’. Make sure to enter a number that is greater than or equal to 1 as the calculator requires this for its calculations. The input should be a whole number, as indicated by the step value of 1.

  2. Enter the Second Number (b): Similarly, find the input field labeled ‘Second Number (b)’. Enter another whole number that is at least 1. This number will be used alongside your first input to perform calculations.

Step 2: Calculate the Results

After entering your numbers, the Euclidean Algorithm Calculator will provide several results. These results are automatically calculated based on the inputs given:

  • Greatest Common Divisor (GCD): This value represents the largest positive integer that divides both inputs without leaving a remainder. It is calculated using the Euclidean algorithm.

  • Least Common Multiple (LCM): The calculator determines the smallest positive integer that both input numbers divide without leaving a remainder. The formula applied is abs(numberA * numberB) / gcd(numberA, numberB).

  • Bézout’s Identity Coefficients (x and y): These coefficients satisfy the equation ax + by = gcd(a, b). The calculator computes both coefficients and displays their values.

  • Are Numbers Coprime?: Discover if the input numbers are coprime, that is, if their GCD equals 1. The result will be either ‘Yes’ or ‘No’, indicating their coprime status.

Conclusion

By following these steps, you can efficiently use the Euclidean Algorithm Calculator to perform a variety of calculations relating to the properties of two numbers. Whether you’re verifying divisibility, finding common multiples, or exploring number theory properties, this calculator provides a comprehensive suite of tools.