Been Clockin' Around ?

Algebra Level pending

Consider a normal clock. If we measure the angle between the two hands the hour hand and the minute hand from clockwise of hour hand ( for example if it is 1: 30 pm then the angle between the hour and minute hand will be considered from right of hour hand that is clockwise from hour hand ) and supposing that at any particular time when any of the two hands that is the hour and the minute hand are not pointing exactly to any of the twelve markings in the the clock rather when they both point between any two adjacent markings and subtend a angle of p degrees such that p is a natural number then let the time be x : y ( x hours and y minutes ) then surely y would not be a natural number rather it would be a fraction ( if and only if we measure it very accurately and precisely ). Let y = a / b where a could be any natural number but b would always be constant. What is the value of b?

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