LCM & GCD Calculator

LCM & GCD Calculator

LCM & GCD Calculator

Enter 2 to 5 positive integers (separated by commas, spaces, or new lines) to find their Least Common Multiple (LCM) and Greatest Common Divisor (GCD).

Results

Enter a set of integers to find their LCM and GCD.

ⓘ Definitions:

  • GCD (Greatest Common Divisor): Also known as GCF (Greatest Common Factor), it's the largest positive integer that divides each of the integers without a remainder.
  • LCM (Least Common Multiple): The smallest positive integer that is a multiple of all the integers. Often used to find a common denominator for fractions.

Usa esta calculadora de LCM GCD Calculator, LCM, GCD, Least Common Multiple, Greatest Common Divisor para obtener estimaciones claras y rápidas. Prueba un ejemplo pequeño para entender el efecto de cada variable.

Overview

Our free online LCM GCD Calculator helps you quickly find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) for any set of numbers. This powerful tool is ideal for students, educators, and anyone needing accurate LCM and GCD calculations. Simply input your numbers to instantly get both results, simplifying complex mathematical problems. ✨

How to Use This Calculator

  1. Enter your numbers into the input field, separated by commas or spaces. For example, “12, 18, 24”.
  2. Click the “Calculate” button to process your input.
  3. View the results for both the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) displayed instantly.

Worked Example

Let’s find the LCM and GCD for the numbers 15, 20, and 25 using our calculator in 2025.

First, input “15, 20, 25” into the calculator. Upon clicking ‘Calculate’, the tool will determine the prime factors for each number. For 15 (3×5), 20 (2²×5), and 25 (5²), the Greatest Common Divisor (GCD) is 5, as it’s the largest factor common to all three. The Least Common Multiple (LCM) is 300, which is the smallest number divisible by 15, 20, and 25 (2²×3×5² = 4×3×25 = 300). This demonstrates how the calculator efficiently provides both values.

Assumptions & Limitations

  • This LCM GCD Calculator assumes all input values are positive integers. Negative numbers, decimals, or fractions are not supported.
  • The calculator is designed for a reasonable number of inputs. Extremely large sets of numbers or very large individual numbers might impact performance.
  • Results for the Least Common Multiple and Greatest Common Divisor are calculated using standard mathematical algorithms, ensuring accuracy for valid inputs.
  • Users should ensure numbers are correctly separated (e.g., by commas or spaces) to avoid input errors.

Frequently Asked Questions

Q: What is the Least Common Multiple (LCM)?
The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of all the integers. For example, the LCM of 4 and 6 is 12.

What is the Greatest Common Divisor (GCD)?
The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. For example, the GCD of 12 and 18 is 6.

How do you find the LCM and GCD of two numbers?
You can find LCM and GCD using prime factorization (listing prime factors and multiplying common/unique ones) or by listing multiples/divisors. For two numbers, the product of the numbers is equal to the product of their LCM and GCD.

Is there a relationship between LCM and GCD?
Yes, for any two positive integers ‘a’ and ‘b’, the product of their Least Common Multiple (LCM) and Greatest Common Divisor (GCD) is equal to the product of the numbers themselves: $LCM(a, b) times GCD(a, b) = a times b$.

Last updated 2025