140 revolutions.

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.