LCM Calculator

Calculate the Least Common Multiple of two or more integers. See the step-by-step prime factorization method, first common multiples, and verification.

---

How It Works

The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the given numbers. For example, LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6.

Prime Factorization Method

This calculator finds the LCM using prime factorization. Each number is broken down into its prime factors, then the LCM is built by taking the highest power of each prime that appears in any factorization.

For example, LCM(12, 18):

1. 12 = 2² × 3
2. 18 = 2 × 3²
3. LCM = 2² × 3² = 4 × 9 = 36

Practical Uses

The LCM is used in many real-world scenarios:

• Adding and subtracting fractions with different denominators
• Finding when periodic events will coincide (scheduling problems)
• Determining gear ratios and synchronization cycles
• Solving problems involving repeating patterns

---

Feedback