GRE Arithmetic question?

Question

"In a certain medical group, Dr. Schwartz schedules appointments to begin 30 minutes apart, Dr. Ramirez schedules appointments to begin 25 minutes apart, and Dr. Wu schedules appointments to begin 50 minutes apart. All three doctors schedule their first appointments to begin at 8:00 in the morning, which are followed by their successive appointments throughout the day without breaks. Other than at 8:00 in the morning, at what times before 1:30 in the afternoon do all three doctors schedule their appointments to begin at the same time?" the guide's explanation was the following "y examining the pattern of beginning times for the three types of appointments, you can see that the times will coincide when the number of minutes after 8:00 in the morning is a common multiple of 30, 25, and 50. The least common multiple of 30, 25, and 50 is 150, which represents 150 minutes, or 2.5 hours. So the times coincide every 2.5 hours after 8:00 in the morning, that is, at 10:30 in the morning, at 1:00 in the afternoon, and so on. The correct answer consists of 10:30 am and 1:00 pm " the only way I am approaching this question is through actually drawing the clock and recording each and every appointment. The approach the guide decided to use which is the "multiple" rule was not intuitive to me. Any inputs?

Answer 1

The least common multiple - LCM - is a "rule" taught in elementary arithmetic. It is not intuitive.