KEVOS® MAKEOS · Mathematics
Prime Factors, Greatest Common Divisor and Least Common Multiple
What are the prime factors of these numbers, and their greatest common divisor and least common multiple?
Prime factorisation, greatest common divisor and least common multiple of two or three whole numbers, for gear tooth counts, hunting-tooth ratios, change gears and repeat cycles.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| First number | First whole number (for example gear teeth). | |
| Second number | Second whole number. | |
| Third number (0 = not used) | Optional third whole number. |
Method and formulas
- Prime factors by trial division.
- GCD by Euclid’s algorithm; LCM = a × b ÷ GCD (extended to three numbers).
- Two gears form a hunting-tooth pair when their GCD is 1 (every tooth meets every other tooth).
- Example: 72 = 2 × 2 × 2 × 3 × 3 and 30 = 2 × 3 × 5; GCD 6, LCM 360.
Limitations
- Whole numbers up to one billion.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check that a gear pair has a hunting-tooth ratio
- Factor a ratio into change gears
- Find when two cycles repeat together
Who it is for
- Gear designers
- Machinists
- Engineers
What you get
- Prime factors of each number
- Greatest common divisor
- Least common multiple
- Hunting-tooth check for two gears
Interpreting the result
- A GCD of 1 between gear tooth counts spreads wear evenly; a large common factor repeats the same tooth contacts.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 20–29. Topic reference; no source tables or recommended settings are reproduced.
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