🔢 GCD and LCM Calculator
Calculate GCD and LCM for any set of numbers
📌 Definitions
- GCD: Largest integer that divides all numbers exactly
- LCM: Smallest positive integer divisible by all numbers
- GCD × LCM = a × b (for two numbers only)
GCD and LCM Calculator Explained
This tool finds the greatest common divisor (GCD) and the least common multiple (LCM) for a set of whole numbers. Enter two or more numbers and it returns both results instantly, saving you from listing factors and multiples by hand. It is useful for math students, teachers, and anyone working with fractions or ratios.
The greatest common divisor is the largest number that divides all your inputs evenly. The least common multiple is the smallest number that every input divides into without a remainder. For example, the GCD of 12 and 18 is 6, while their LCM is 36. The two ideas are closely linked through the rule that the product of the numbers equals the GCD multiplied by the LCM.
Where You Use Them
GCD is essential for simplifying fractions to their lowest terms, since you divide the numerator and denominator by their greatest common divisor. LCM is needed when adding or subtracting fractions, because you must rewrite them over a common denominator. Both also appear in scheduling problems, such as finding when two repeating events line up again.
To use the calculator, type your numbers separated by spaces or commas and read off both values. It handles several numbers at once, making it a quick reference for homework and classroom examples.