**Answer:** 230 revolutions.

We are after a number such that (revolutions * largest cog) / (every small cog) is an integer. This is easily achieved by looking at the cogs' prime factors:

102 = 2 * 3 * 17

60 = 2 * 2 * 3 * 5

46 = 2 * 23

34 = 2 * 17

So

revolutions * 102

-----------------------

2 * 2 * 3 * 5 * 23 * 17

revolutions * 2 * 3 * 17

= ------------------------

2 * 2 * 3 * 5 * 23 * 17

revolutions

= -----------

2 * 5 * 23

Which means revolutions = 230. QED