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Key Features
Instant Calculation
Get accurate results in real time with our optimized algorithm.
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Finding the GCD or LCM of just two numbers is simple, but extending that to a longer list of numbers means repeating the process pairwise — easy to get wrong by hand. This calculator finds both the GCD and LCM of any list of numbers at once, by reducing the list pairwise with the Euclidean algorithm, with a full step-by-step solution.
How it works
Enter a comma-separated list of numbers. The calculator finds the GCD of the whole list by repeatedly applying the Euclidean algorithm pairwise, carrying the running result forward, and does the same for the LCM.
- Enter numbers (comma-separated).
- Click Calculate to see your results.
Examples
GCD and LCM of 12, 18, and 24
For the list 12, 18, 24, the GCD is 6 and the LCM is 72.
Who should use it
- Finding a common denominator when adding three or more fractions at once.
- Scheduling problems where multiple repeating events need to be synchronized (finding when they next align).
Industry applications
- Mathematics education
- Scheduling and operations planning
Advantages
- Handles any list of 2 to 10 numbers in one calculation, rather than requiring repeated pairwise steps.
- Uses the exact Euclidean algorithm, not an approximation.
Limitations
- Limited to whole, positive numbers and a maximum of 10 values per calculation.
Common mistakes to avoid
- Entering fewer than 2 numbers or non-whole numbers, which the calculator can't process.
- Assuming the LCM of a list is just the product of all the numbers — it's only true when every pair is coprime.
Best practices
- When working with fractions, use this calculator's LCM result as the common denominator when adding or subtracting more than two fractions at once.
Tips
- For scheduling problems (like "every how many days do three repeating events coincide"), the LCM of the individual intervals gives the answer directly.