Math Quiz: All around the clock

At 12 o'clock the minute hand and the hour hand of an analogue clock point to the same position. This happens at other times as well. Can you figure out a rule for calculating those times?

Additionally, it may also be possible that all three hands (hours, minutes and seconds) overlap. When does this happen?

Note: This clock-riddle is pretty close to the relationship between day length, the length of a whole year and the duration of a single turn of the rotating earth.