Now if hour and minute hands of a clock form an angle of 18 degree. Minimum amount of time to repeat the same situation?

Question

At a given time, the hour and minute hands of a clock form an angle of 18 degree exactly . What is the minimum amount of time it takes that this will be the case again?

Answer 1

There are 4 times in a 12 hour time span where the angle between the hour and the minute hand exactly equals 18 degrees, they are: 3:13:5.5, 4:25:5.5, 5:24:00, & 6:36:00.
The gap between 5:24 and 4:25 is the least and it turns out to be 59 minutes.
but the times 4:25 and 3:13 have a small error equal to 5.454 seconds ie., the exact times are 4:25:5.454 and 3:13:5.454 when the angle between the hour and the minute hand is 18 degrees. If this is not included then only 5:24 and 6:36 will be left which have a time gap of exactly 72 minutes.