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Puzzle - Hint

The BrainBashers mechanical computer is a very sensitive device, in consists of four sequential cog wheels which are in constant mesh.

The largest cog has 63 teeth and the others have 42, 35 and 27 respectively.

By accident, Daniel started to rotate the largest cog.

How many revolutions must he rotate the largest cog make before the computer is back in its starting position with all of the cogs where they started?

Puzzle Cogs

 [Ref: ZTLC] © Kevin Stone

Hint: Try breaking each cog size into prime factors.

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