cog wheels

[revision]

I have a machine with 4 cog wheels in linear mesh. The largest has 165 teeth and the others in line have 45, 40 and 32 teeth. How many revolutions of must the largest cog make before each cog is back in its original position ?
Please

[ChuckFickens]

as you have the machine paint little dots on the cogs spin that handle and see.

[buildersmate]

96, by which time the 45-tooth wheel has done 352 revolutions, the 40-tooth wheel has done 396 revolutions and the 32-tooth wheel has done 495 revolutions.
Trouble is, the school will probably want to see my workings for you to get the marks.

[beso]

It is maeant as a factorisation puzzle.

As a matter of interest gears which are not used to synchronise shafts such as the 1:2 ration of the camgears are invariably made of co-prime ratios. Using prime numbers ensures that every tooth in the drive gear meshes with every tooth on the driven gear. This ensures the smoothest finish and even wear is maintained on every tooth.