GCD & LCM Calculator

Calculate the Greatest Common Divisor and Least Common Multiple of any set of numbers with real-time results.

Number Processing

Enter multiple numbers separated by spaces or commas to begin analysis.

Numbers InputMin 2 required

v_1

v_2

v_3

GCD & LCM synthesis active

GCD

100

Analyzed 3 data integers

LCM

6,000

Mathematical synthesis complete

GCD & LCM DERIVATION

Mathematical step-by-step logic

Step 1: Analysis of next number 500

Finding GCD of 500 and 300 using Euclidean algorithm:

500 = 300 × 1 + 200

300 = 200 × 1 + 100

200 = 100 × 2 + 0

Resulting GCD = 100

Intermediate GCD so far = 100

Intermediate LCM so far = 1,500

Step 2: Analysis of next number 400

Finding GCD of 400 and 100 using Euclidean algorithm:

400 = 100 × 4 + 0

Resulting GCD = 100

Final Calculation for LCM:

Extension of mathematical identity to 3 numbers complete.

GCD(300, 500, 400) = 100

LCM(300, 500, 400) = 6,000

What are GCD and LCM?

The Greatest Common Divisor (GCD) of a set of numbers is the largest positive integer that divides each of the integers. The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all numbers in the set.

How it Works

Calculation Protocol

For two numbers, GCD(a, b) is calculated using the Euclidean algorithm. The LCM is then found using the identity: LCM(a, b) = |a × b| / GCD(a, b). For multiple numbers, these operations are applied sequentially across the entire set.

Frequently Asked Questions