LCM, GCD & Factorial Calculator
Math Calculator: Find LCM, GCD & Factorial Instantly
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Factorials above 100! are too large to compute accurately in this calculator.
Enter up to 20 positive integers separated by commas.
Enter up to 20 positive integers separated by commas.
About LCM,GCD & Factorial
Factorial (n!) - Limited to 100!
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It's denoted by n!.
Example: 5! = 5 × 4 × 3 × 2 × 1 = 120
Due to the extremely large size of factorial results, this calculator limits calculations to 100! (which is about 9.33×10¹⁵⁷).
Greatest Common Divisor (GCD) for Multiple Numbers
The GCD of multiple integers is the largest positive integer that divides each of the integers without leaving a remainder.
Example: GCD of 56, 98, and 42 is 14
This calculator can find the GCD of up to 20 numbers at once using the Euclidean algorithm.
Least Common Multiple (LCM) for Multiple Numbers
The LCM of multiple integers is the smallest positive integer that is divisible by all the numbers.
Example: LCM of 12, 18, and 24 is 72
This calculator can find the LCM of up to 20 numbers at once using the relationship between GCD and LCM.
How to Use This Calculator
- Factorial: Enter a single number between 0 and 100
- GCD/LCM: Enter multiple numbers (up to 20) separated by commas
- Numbers can include spaces (e.g., "12, 18, 24" or "12,18,24")
- Click the calculate button to see results
Frequently Asked Questions
LCM (Least Common Multiple)
The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by all of them. Example: LCM of 4 and 6 is 12.
Our calculator uses the prime factorization method (listing all prime factors and taking the highest powers) or the division method for quick results.
You can calculate LCM for 2 to 20 numbers at once.
GCD (Greatest Common Divisor)
The Greatest Common Divisor (GCD) is the largest number that divides two or more integers without a remainder. Example: GCD of 8 and 12 is 4.
No, GCD is only defined for positive integers. Enter whole numbers only.
We use the Euclidean algorithm, the most efficient method for large numbers.
Factorials
The factorial of a non-negative integer (n!) is the product of all positive integers ≤ n. Example: 5! = 5 × 4 × 3 × 2 × 1 = 120.
We support factorials up to 100! (≈ 9.33 × 10¹⁵⁷). Larger values may return "Infinity" due to JavaScript limitations.
No, factorials are only defined for non-negative integers. Use the Gamma function for non-integers (not supported here).
General Questions
Yes! 100% free
No data is stored—all calculations happen in your browser.
Absolutely! Perfect for students and teachers needing quick verification.
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