GCD & LCM Calculator

Calculate GCD and LCM with Euclidean algorithm visualization and step-by-step process

Overview

The GCD & LCM Calculator finds the Greatest Common Divisor and Least Common Multiple of numbers using the efficient Euclidean algorithm. Watch the step-by-step process as the algorithm repeatedly divides numbers until it finds the GCD, then use the relationship GCD × LCM = a × b to calculate the LCM.

Tips

  1. Watch the Euclidean algorithm: Follow each division step as it replaces the larger number with the remainder until reaching zero - the last non-zero remainder is your GCD.

  2. Use the GCD-LCM relationship: Once you have the GCD, calculate LCM quickly using the formula LCM(a,b) = (a × b) / GCD(a,b) rather than finding it from scratch.

  3. Simplify fractions with GCD: Divide both the numerator and denominator by their GCD to reduce any fraction to its simplest form.

  4. Find common denominators with LCM: When adding fractions with different denominators, the LCM gives you the smallest common denominator to use.

  5. Check for coprime numbers: If GCD = 1, the numbers are relatively prime (share no common factors), which means their LCM equals their product.