Welcome to our Least Common Multiple (LCM) Calculator. This tool instantly finds the smallest positive number that is a multiple of two integers. This is the exact same math used to find the Least Common Denominator (LCD) when working with fractions.
Below the tool, we provide a full educational guide on how to calculate LCM manually using prime factorization and the listing method.
Use the LCM / LCD Calculator
Enter two numbers to find their lowest common multiple.
LCM / LCD Calculator
How to Use This Tool
This calculator is designed for students, teachers, and developers.
- Enter the first number (e.g., 4).
- Enter the second number (e.g., 6).
- Click “Calculate LCM”.
- The result (e.g., 12) will appear instantly.
What is the Least Common Multiple (LCM)?
The Least Common Multiple of two numbers is the smallest non-zero number that is a multiple of both. In other words, it is the first number that both of your integers can divide into evenly.
Example: LCM of 4 and 6
- Multiples of 4: 4, 8, 12, 16, 20, 24…
- Multiples of 6: 6, 12, 18, 24, 30…
Both 12 and 24 are common multiples, but 12 is the smallest (least). Therefore, LCM(4, 6) = 12.
Is LCM the same as LCD?
Mathematically, yes. The Least Common Denominator (LCD) is simply the LCM applied to the bottom numbers (denominators) of fractions. If you need to add 1/4 + 1/6, you must find the LCD of 4 and 6, which is 12.
Real-World Applications
Why does this matter outside of math class?
1. Scheduling and Cycles
Imagine two lights blinking at different intervals. Light A blinks every 4 seconds. Light B blinks every 6 seconds. When will they blink at the exact same time?
Answer: In 12 seconds (the LCM). This logic is used in computer scheduling and manufacturing.
2. Comparing Fractions
You cannot easily compare 3/8 and 5/12 until they have the same denominator. You use the LCM of 8 and 12 (which is 24) to convert them.
How to Calculate LCM Manually
Method 1: Prime Factorization
This is the most reliable method for schoolwork.
Task: Find LCM(12, 18)
- Factor 12: 2 × 2 × 3 (or 22 × 31)
- Factor 18: 2 × 3 × 3 (or 21 × 32)
- Rule: For each prime factor, take the highest power that appears in either list.
- We take 22 (4) and 32 (9).
- Multiply them: 4 × 9 = 36.
Method 2: The GCD Formula
If you already know the Greatest Common Divisor (GCD), you can use this simple formula:
LCM(a, b) = (a × b) ÷ GCD(a, b)
Example: LCM(12, 18)
- a × b = 12 × 18 = 216
- GCD(12, 18) = 6
- 216 ÷ 6 = 36
Frequently Asked Questions
Q: Can I use this for more than two numbers?
A: Yes, the principle is the same. For three numbers, find the LCM of the first two, then find the LCM of that result and the third number.
Q: Is the LCM always larger than the numbers?
A: It is always greater than or equal to the largest number. For example, LCM(2, 8) is 8.