1. A grandfather clock is a machine that has 4 cogs constantly in mesh with each other. The largest cog has 338 teeth and the others have 130, 160 and 52 respectively. How many revolutions must the largest cog make before each of the cogs is back in its starting position? (Hint: how many revolutions would you need to make to get all cogs back to the starting position if you had two gears with 3 and 4 teeth respectively? Use this to generalize your findings).
+23251 4 cogs with 338 teeth, 130 teeth, 160 teeth, and 52 teeth are in mesh with each other.
How many revolutions must the largest cog make before each of the cogs is back in its starting position?
Find the prime factorization of each of the numbers:
338 = 2 x 132
130 = 2 x 5 x 13
160 = 25 x 5
52 = 22 x 13
Find the least common multiple: 25 x 5 x 132 = 27040
27040 / 338 = 80 revolutions <--- answer
27040 / 130 = 208 revolutions
27040 / 160 = 169 revolutions
27040 / 52 = 520 revolutions
