Exact patterns · One shared tick unit
When do your cycles line up?
Enter a period and phase for each ideal repeating cycle. Find the least nonnegative common tick and its repeat interval, or see exactly why the phases cannot meet.
Free · Exact integers · Browser-localYour cycle rows
A row 5,2 means every integer tick congruent to 2 modulo 5: … −3, 2, 7, 12, 17 … . A phase is a repeating offset, not a first-ever activation.
Exact alignment notes
Least nonnegative common tick
- Exact repeat interval
- Entered rows
First four nonnegative alignments
A valid no-alignment result
The conflict is against the combined earlier rows. Your syntax can be valid while the cycle system has no common integer tick.
| Row | Period | Entered phase | Normalized phase |
|---|
Edits clear the old result and exports immediately. Calculate again for current notes. Large answers are decimal integers, with no floating-point rounding.
Offsets matter
Periods 6 and 8 can meet at tick 20 with phases 2 and 4. A least common multiple alone cannot find this first alignment.
No meeting can be exact
A phase of 0 modulo 4 requires an even tick. A phase of 1 modulo 6 requires an odd tick. No integer satisfies both.
Tick 0 is allowed
If every cycle includes the origin, the least nonnegative alignment is 0. The result explains the next strictly positive tick separately.
This is an abstract integer-pattern calculator. It does not model real clock drift, dates, timezones, reminders, deadlines, electrical systems or safety-critical scheduling.