LCM Calculator
Calculate the Least Common Multiple (LCM) of two or more numbers, with a step-by-step prime factorization breakdown.
Numbers
#1
#2
LCM
12
Prime Factorization Breakdown
| Number | 2 | 3 |
|---|---|---|
| 4 | 2 | 0 |
| 6 | 1 | 1 |
| Highest Power | 2 | 1 |
How to Calculate the LCM (Least Common Multiple)
The Least Common Multiple (LCM) of a set of numbers is the smallest positive number that is exactly divisible by every number in the set. This calculator finds the LCM using prime factorization: it breaks each number down into its prime factors, then takes the highest power of every prime that appears across all the numbers and multiplies them together.
Add two or more numbers below and the calculator shows both the LCM and the step-by-step prime factorization used to find it.
Example
For 4 and 6: 4 = 2², and 6 = 2 × 3. Taking the highest power of each prime (2² and 3¹) gives LCM = 2² × 3 = 12 — the smallest number divisible by both 4 and 6.
Common Use Cases
- Finding a common denominator when adding or subtracting fractions.
- Solving word problems about repeating events, like when two flashing lights next align.
- Scheduling problems involving multiple recurring intervals.
FAQs
How is LCM different from GCD?
LCM (Least Common Multiple) is the smallest number that all your numbers divide into evenly, while GCD (Greatest Common Divisor) is the largest number that divides evenly into all of them. They're related by the formula LCM(a,b) × GCD(a,b) = a × b for two numbers.
Can I find the LCM of more than two numbers?
Yes — add as many rows as you need. The prime factorization method used here scales naturally to any number of values by taking the highest power of each prime across every number entered.
What happens if I enter a 0 or a negative number?
LCM is only defined for positive integers, so zero and negative entries are excluded from the calculation entirely — only enter positive whole numbers for a meaningful result.