Brain Teasers
Wheel Machine
I have a machine which has four cog wheels in constant mesh. The largest cog has 242 teeth and the others have 160, 64 and 22 respectively. How many revolutions must the largest cog make before each of the cogs is back in its starting position?
Answer
160 revolutions.The least common multiple of 242=2*11^2, 160=2^5*5, 64=2^6 and 22=2*11 is 2^6*5*11^2=38720.
38720/242=160.
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