Free GCD and LCM calculator using the Euclidean algorithm. Find the greatest common divisor and least common multiple with steps.
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Finding the Greatest Common Divisor (GCD) or Least Common Multiple (LCM) of two numbers is essential for simplifying fractions, solving equations, and many practical applications. Our calculator finds both values instantly using the efficient Euclidean algorithm.
The GCD is the largest number that divides evenly into two or more numbers. The LCM is the smallest number that is a multiple of two or more numbers. These concepts are fundamental in number theory, fractions, and solving real-world problems involving cycles and intervals.
Key Relationship
Use GCD to reduce fractions to their lowest terms.
Use LCM to find the common denominator when adding fractions.
Find when cyclical events will coincide.
Divide items into equal groups of the largest possible size.
Get both GCD and LCM in a single operation.
Use the GCD to simplify fractions and the LCM to find a common denominator when adding fractions.
See the step-by-step calculation process.
GCD is used to simplify fractions to their lowest terms, find common denominators, and solve problems involving equal distribution or grouping.
LCM is used to add or subtract fractions with different denominators, and to solve problems involving repeating cycles or schedules.
It's an efficient method to calculate GCD. Repeatedly divide the larger number by the smaller and take the remainder until you reach zero. The last non-zero divisor is the GCD.
The fastest method is the Euclidean algorithm: divide the larger number by the smaller and keep the remainder, then repeat using the previous divisor and the remainder until the remainder is 0. The last non-zero remainder is the GCD. For example, GCD(48, 18): 48 = 18×2 + 12, then 18 = 12×1 + 6, then 12 = 6×2 + 0, so the GCD is 6.