Number Theory Solver

LCM Calculator

Calculate Least Common Multiple (LCM) of multiple numbers instantly with prime factor ratio derivations.

Enter Numbers

LCM Result

180

Step-by-Step LCM derivation:

lcm(12, 15) = (12 × 15) / gcd(12, 15) = 180 / 3 = 60 lcm(60, 18) = (60 × 18) / gcd(60, 18) = 1080 / 6 = 180

What is the LCM Calculator?

The Least Common Multiple (LCM) Calculator finds the smallest positive integer that is perfectly divisible by two or more numbers. Finding the LCM is the mandatory first step when trying to add or subtract fractions with different denominators.

How It Works (Formula)

The most computationally efficient way to find the LCM of two numbers is to multiply their absolute values together, and then divide that product by their Greatest Common Factor (GCF), which is found via the Euclidean algorithm.

$$ \text{LCM}(a,b) = \frac{|a \times b|}{\text{GCF}(a,b)} $$

The direct mathematical relationship between the LCM and the GCF.

How to Use It

Enter your data set of whole numbers, separated by commas (for example: 4, 6, 15). The calculator will instantly process the relationship between the numbers and output the lowest possible common multiple.