Amovie theater has two screens and shows it’s movie continuously. a 30 minute documentary is shown on one screen. a 90 minute feature is shown on the other screen. if both movies begin at noon, how many minutes will pass before both movies begin again at the same time?

To answer this item, we let x be the number of times that the 30-minute documentary is shown and y be the number of times that the 90-minute documentary is shown. By the given scenario in the item, we have,
   
      30x = 90y

The least common multiple (LCM) of the numerical coefficients of the equation is equal to 90. Thus, 90 minutes will pass and the documentaries will start again.