Calculadora de MDC e MMC
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
MMC(a,b) = (a × b) / MDC(a,b)
About this calculator
The GCD and LCM Calculator is an online tool that computes the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two integers. The GCD is the largest number that divides both numbers without a remainder, while the LCM is the smallest number that is a multiple of both. The calculator uses the Euclidean algorithm to find the GCD and then applies the formula LCM(a,b) = (a × b) / GCD(a,b) to obtain the LCM.
To use the calculator, simply enter two positive integers in the designated fields and click 'Calculate'. The result will display both the GCD and LCM. This tool is useful for students, teachers, and professionals who need to solve divisibility problems, fractions, or find common denominators. It is especially helpful in basic math and number theory tasks.
Common use cases include simplifying fractions (dividing numerator and denominator by the GCD), finding the least common denominator for adding or subtracting fractions (using the LCM), and solving grouping or periodicity problems. For example, if two tasks repeat every 6 and 8 days, the LCM indicates when they will occur together again (24 days).
Cautions: the calculator only accepts positive integers. Negative numbers or zero may produce incorrect results. Additionally, for very large numbers, the calculation may require more processing, but the tool is optimized for most cases. Always double-check the entered values before calculating.
Frequently asked questions
What do GCD and LCM mean?
GCD stands for Greatest Common Divisor, the largest number that divides two numbers without a remainder. LCM stands for Least Common Multiple, the smallest number that is a multiple of both.
How to calculate GCD and LCM manually?
The GCD can be calculated using the Euclidean algorithm (successive divisions) or prime factorization. The LCM can be obtained by prime factorization or the formula LCM = (a × b) / GCD.
Can I use negative numbers or zero?
No. The calculator is designed for positive integers. For negative numbers, consider the absolute value. Zero is not accepted because the GCD with zero is undefined.
What is the practical use of GCD?
GCD is used to simplify fractions, divide items into equal groups, and solve divisibility problems. For example, dividing 12 apples and 18 oranges into equal baskets without mixing: the GCD (6) indicates 6 baskets.
What is the relationship between GCD and LCM?
For two numbers, the product of the GCD and the LCM equals the product of the numbers. That is, GCD(a,b) × LCM(a,b) = a × b. This relationship is used by the calculator.