What are GCD and LCM?

The Greatest Common Divisor (GCD) — also called the Greatest Common Factor (GCF) or Highest Common Factor (HCF) — is the largest positive integer that divides both numbers without leaving a remainder. For example, the GCD of 36 and 48 is 12, because 12 is the biggest number that goes into both evenly. The GCD is fundamental to simplifying fractions: to reduce 36/48, you divide both numbers by their GCD of 12, giving 3/4.

The Least Common Multiple (LCM) is the smallest positive integer that is a multiple of both numbers. The LCM of 4 and 6 is 12, because 12 is the first number that appears in both the four-times table and the six-times table. The LCM is essential whenever you need a common denominator to add or subtract fractions — for example, to add 1/4 + 1/6 you convert both to twelfths (3/12 + 2/12 = 5/12). The two values are linked by a simple identity: LCM(a, b) = |a × b| ÷ GCD(a, b).

How to Use the LCM & GCD Calculator

Enter the two positive integers you want to analyse in the Number A and Number B fields side by side. You can type in either field and switch between them with Tab. When you are ready, press the green CALCULATE button or hit Enter from either input. The CRT display shows the GCD on the top row and the LCM directly below — both rendered in large glowing numerals for easy reading.

The calculator accepts only non-negative integers and will show a clear error message if you enter a decimal, a negative number, or leave a field blank. Changing either input automatically resets the display so the previous result never lingers to cause confusion. This tool uses Euclid's division algorithm to compute the GCD in milliseconds, making it equally fast for small everyday numbers and very large integers.