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Puzzle - Hint

I have a machine which has four sequential cog wheels in constant mesh.

The largest cog has 21 teeth and the others have 17, 12 and 10 respectively.

What is the fewest number of revolutions the largest cog must make so that all of the cogs are back in their starting position?

Cogs

 [Ref: ZOUQ] © Kevin Stone

Hint: Try breaking each cog size into prime factors.

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