Calculator
Enter at least two integers. Separate values with commas, spaces, or new lines.
Example Data Table
| Input Set | GCD | LCM | Why It Helps |
|---|---|---|---|
| 24, 36, 60 | 12 | 360 | Shows common classroom multiples and factors. |
| 15, 25 | 5 | 75 | Good for learning pair relationships. |
| 8, 12, 20 | 4 | 120 | Shows reduction across three values. |
| 7, 11, 13 | 1 | 1001 | Demonstrates co-prime inputs clearly. |
Formula Used
Greatest Common Divisor: The GCD is the largest positive integer that divides every input without leaving a remainder.
Euclidean Method: Repeatedly replace the pair (a, b) with (b, a mod b) until the remainder becomes zero.
Least Common Multiple: For two integers, LCM(a, b) = |a × b| ÷ GCD(a, b).
Multiple Inputs: Apply both rules from left to right until every number has been included.
Zero Convention: This calculator reports GCD(0, 0) = 0 and any LCM containing zero as 0.
How to Use This Calculator
- Enter two or more integers in the numbers box.
- Use commas, spaces, or line breaks as separators.
- Choose your preferred chart type.
- Turn on sorting, duplicate removal, or step display if needed.
- Press the calculate button.
- Read the summary, graph, and factorization table above the form.
- Download the result as CSV or PDF when needed.
FAQs
1. What is the difference between GCD and LCM?
GCD is the biggest whole number dividing all inputs exactly. LCM is the smallest positive whole number that every input can divide without remainder.
2. Can I enter more than two numbers?
Yes. The calculator accepts several integers and reduces them step by step, so you can find the shared GCD and shared LCM for longer lists.
3. Does the order of numbers matter?
No. GCD and LCM values stay the same regardless of order. Sorting only changes how the list appears and how the reduction steps are displayed.
4. What happens with negative numbers?
The calculator uses absolute values for the math because GCD and LCM are usually reported as non-negative results. Negative signs do not change the final magnitudes.
5. How does zero affect the answer?
Zero can make the LCM become zero. For GCD, zero works with the other numbers normally, and the calculator reports GCD(0, 0) as zero by convention.
6. Why show prime factorization?
Prime factors help explain where the GCD and LCM come from. They are useful for teaching, checking homework, and understanding repeated prime powers clearly.
7. Why does the graph include GCD and LCM?
The graph makes comparisons easier. You can quickly see whether the shared divisor is small, or the common multiple is much larger than the inputs.
8. When should I use this calculator?
Use it during lessons, revision, worksheets, fraction simplification, ratio work, scheduling problems, or anywhere you need a fast and reliable common factor or multiple check.