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).

Please use GCF to solve