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Puzzle Details

The BrainBashers mechanical computer is a very sensitive device, it consists of interlocked toothed gear cogs.

The largest cog has 168 teeth and the others have 49, 32 and 15 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?

If we break each wheel into its prime factors, we get:

168= 2 x 2 x 2 x 3 x 7
49 = 7 x 7
32 = 2 x 2 x 2 x 2 x 2
15 = 3 x 5

So

revolutions x 168
---------------------------------
2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7

revolutions x 2 x 2 x 2 x 3 x 7
---------------------------------
2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7

revolutions
-------------
2 x 2 x 5 x 7

revolutions
-------------
140

Which means revolutions = 140. QED.

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