When will two repeating schedules coincide again?
The least common multiple identifies a shared positive interval when both events start together and repeat at exact whole-number intervals.
GCD and LCM calculator →List a small example
One signal repeats every 12 seconds and another every 18 seconds. Their positive event times are 12,24,36,… and 18,36,54,…. The first common time is 36 seconds. The LCM tool returns 36 for 12 and 18. It is not enough to add the two intervals; 30 seconds is not a multiple of either interval.
Convert to a shared exact unit
An interval of 1.5 minutes and another of 2 minutes can be expressed as 90 and 120 seconds. Their LCM is 360 seconds, or 6 minutes. Integer input is required, so converting both intervals is better than rounding 1.5 minutes to 2. Changing units consistently preserves the timing relationship; rounding an interval changes the schedule itself.
Offsets and real schedules need more work
The simple LCM answer assumes the events coincide at the starting time. If one begins later, an offset equation is needed and the first meeting may differ or never occur. Calendar months do not have equal lengths, and real services may have delays or exceptions. Use date or business-day tools for calendar questions rather than treating all months or working weeks as fixed identical intervals. A zero repeat interval is not a meaningful repeating schedule, even though the integer tool accepts one zero.
Try the calculators
- GCD and LCM calculator
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- Ratio calculator
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