Least Common Multiple Calculator

Calculate the LCM of multiple numbers using prime factorization, Euclidean algorithm, or listing multiples with detailed step-by-step solutions.

Enter numbers and choose calculation method

Input Method

Numbers (comma or space separated)

Enter 2-20 positive integers, separated by commas or spaces

Calculation Method

Prime factorization shows the clearest step-by-step process

Quick Examples:

Step 1: Find prime factorization of each number

Step 2: Identify all unique prime factors

Step 3: For each prime, take the highest power

Step 4: Multiply all highest powers together

Example: LCM(12, 18) = LCM(2²×3, 2×3²) = 2²×3² = 36

Formula: LCM(a,b) = (a × b) / GCD(a,b)

For multiple numbers: Apply iteratively

Step 1: Calculate GCD using Euclidean algorithm

Step 2: Apply LCM formula

Example: LCM(12, 18) = (12 × 18) / GCD(12, 18) = 216 / 6 = 36

Step 1: List multiples of each number

Step 2: Find the smallest common multiple

Best for: Small numbers and educational purposes

Example: Multiples of 12: 12, 24, 36, 48...
Multiples of 18: 18, 36, 54, 72... → LCM = 36

• Prime Factorization: Best for understanding, works well with any size numbers

• Euclidean Algorithm: Efficient for programming, good for large numbers

• Listing Multiples: Educational tool, visual for small numbers