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How to Use This Calculator

Enter at least two positive integers in the input fields
Click "Add Number" to include more numbers (up to 6)
Click "Calculate LCM" to find the result
View the step-by-step solution using prime factorization
Use quick examples to see how the calculator works

About LCM (Least Common Multiple)

What is LCM?

The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by all the given numbers without leaving a remainder.

Methods to Find LCM

Prime Factorization: Break numbers into prime factors
Division Method: Divide by common factors
Listing Multiples: List multiples and find common ones
Using GCD: LCM(a,b) = (a × b) ÷ GCD(a,b)

Applications of LCM

Adding fractions with different denominators
Finding common periods in cyclic events
Scheduling problems
Problem solving in mathematics
Computer science algorithms

Example

Find LCM of 12 and 18:
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 4 × 9 = 36

Properties of LCM

LCM of two numbers is always ≥ the larger number
LCM(a, b) × GCD(a, b) = a × b
If one number divides another, LCM is the larger number

LCM is commutative: LCM(a, b) = LCM(b, a)
LCM is associative: LCM(a, LCM(b, c)) = LCM(LCM(a, b), c)
LCM of coprime numbers is their product

LCM Calculator

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Step-by-Step Solution