Four wheels moving 12, 25, 20 and 30 revolutions in a minute starting at a certain point on the circumference downwards. After what interval of time will they come together again in the same position?
(a)30s
(b)20s
(c)15s
(d)45s

• Figure out the prime factorization of each number:
  
  24 = 2 x 2 x 2 x 3
  
  32 = 2 x 2 x 2 x 2 x 2
  
  48 = 2 x 2 x 2 x 2 x 3
  
  52 = 2 x 2 x 13
  
  The greatest common factor is 4, so we can divide 1 minute by 4.
  
  Answer:
  
  They will all be lined up every 15 seconds.
  
  (First wheel will have made 6 revolutions, second 8 revolutions, third 12 revolutions, fourth will have gone 13 revolutions. Since they have all gone a whole number of revolutions, they will be lined up with the points on the circumference all pointing down again.
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