hour and minute hands coincide every 12/11 hours. the numerator suggests dividing that interval into 12. 1/11 hour = 5.4545 minutes = 5 min 27.2727 sec.
at those intervals, hour and minute hands are separated by an integer multiple of 30 degrees, the angle between hour numbers. these include times exactly on the hour.
finding the times of 0, 30, 60, 90, 120, or 180 degree separation is not difficult. it's nice that 12 has many divisors.
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