Clock Math

The GeoGebra below shows a clock with N positions. Starting from the N o'clock, the system will draw lines each time jumping J hours ahead. 1.  Consider N = 12.      (a)  What is the shape of the figure obtained when            (i)   J = 3?            (ii)  J = 4?            (iii) J = 6?      (b)  Which value(s) of J will result in a complete cycle?            [Hint: A complete cycle means the figure visits all the positions.]      (c)  Which property must J have to result in a complete cycle? 2.  Try other values of N and J. See if your answer in question 1(c) is true.