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GCD & LCM Workbench

Find the exact greatest common divisor and least common multiple of a list, with Euclidean steps and a two-number Bézout identity.

Worked examplesBrowser processingTXT · CSV · JSON

Explore the example, or adjust the inputs. Save a project to keep your settings.

A useful starting point

84 and 126 have GCD 42 and LCM 252. The Euclidean rows show the divisions that establish the GCD.

Scope and limits

Up to 50 signed integers of 100 digits each. LCM results are limited to 5,000 digits. Zero conventions are stated with the results.

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Using GCD & LCM Workbench

Find the exact greatest common divisor and least common multiple of a list, with Euclidean steps and a two-number Bézout identity.

Choose a worked example or enter your own values in the labeled controls.
Adjust the available options. Results refresh when you leave a field or choose an option.
Review the result summary, interpretation and calculation table. Check any explicit limits or assumptions.
Copy the text or download TXT, CSV or JSON. Save a project to reopen the same inputs later.

Example

84 and 126 have GCD 42 and LCM 252. The Euclidean rows show the divisions that establish the GCD.

Questions & answers

Can I use negative numbers or zero?

Yes. Signs are ignored for GCD and LCM. Any zero makes the LCM zero; a list consisting only of zeros has GCD zero.

What is the Bézout identity?

For exactly two inputs, the report provides integer coefficients x and y such that ax + by equals their GCD.

Can I save and reopen my settings?

Yes. Save project downloads a JSON file for this tool. Open project restores it; undo and redo work during the current session.

Does the table contain every result?

The table is paginated in groups of 50. Downloads contain all listed rows. The partition tool intentionally caps its example listing while reporting the full exact count.