GCD & LCM Calculator

What is the GCD & LCM Calculator?

The GCD (Greatest Common Divisor) is the largest number that divides two or more numbers without leaving a remainder. The LCM (Least Common Multiple) is the smallest number that both numbers divide into evenly. These two values show up in fraction simplification, scheduling problems, and number theory. CalciHub's calculator finds both at once, you enter the numbers, and it shows you the GCD and LCM with the steps used to reach them.

How Does It Work?

GCD uses the Euclidean Algorithm:

GCD(a, b) = GCD(b, a mod b), repeated until the remainder is 0

LCM uses the relationship between GCD and LCM:

LCM(a, b) = (a × b) / GCD(a, b)

a, b = the two numbers you input

mod = the remainder after division

The Euclidean Algorithm is efficient even for large numbers

How to Use CalciHub's GCD & LCM Calculator

1. Enter the first number in the first field.

2. Enter the second number in the second field.

3. Click Calculate.

4. The GCD and LCM are displayed together with the step-by-step working.

5. For more than two numbers, find GCD or LCM pairwise and apply the same logic repeatedly.

Tip: GCD is particularly useful for simplifying fractions, divide both the numerator and denominator by their GCD to get the fraction in its lowest form.

A Quick Example

Find the GCD and LCM of 36 and 48.

Euclidean Algorithm for GCD:

GCD(48, 36) → 48 mod 36 = 12 → GCD(36, 12) → 36 mod 12 = 0 → GCD = 12

LCM: (36 × 48) / 12 = 1728 / 12 = 144

GCD = 12, LCM = 144

Practically, this means 12 is the largest number that fits evenly into both 36 and 48, and 144 is the smallest number both divide into, useful when aligning two repeating cycles.

Frequently Asked Questions