Solve the problem.
-A cereal manufacturer uses three large overhead bins to hold the three ingredients in one of its cereal mixes. Bin A delivers a premeasured quantity of dried fruit every 21 minutes, bin B delivers raisins every 33 minutes, and bin $C$ delivers flakes every 6 minutes. If they start the morning shift at the same time, how long before they deliver their ingredients at the same time again?
A) 462 minutes
B) 231 minutes
C) 924 minutes
D) 154 minutes

Question

Quizplus · Accepted Answer

To find when the bins deliver their ingredients at the same time again, we need to find the least common multiple (LCM) of their delivery intervals. The intervals are 21 minutes for bin A, 33 minutes for bin B, and 6 minutes for bin C. The prime factorization of these numbers is 21 = 3 * 7, 33 = 3 * 11, and 6 = 2 * 3. The LCM is the product of the highest power of all prime numbers appearing in the factorization, which is 2 * 3 * 7 * 11 = 462. Therefore, they will all deliver their ingredients at the same time again after 462 minutes.

Solve the Problem CCC Delivers Flakes Every 6 Minutes

Solve the Problem $C$ Delivers Flakes Every 6 Minutes