9. A bell rings every 10 minutes and a buzzer sounds every 15 min ites. If the bell and buzzer both sound at 8 a.m., what is the next time that they will both go off at the same time?

To determine when the bell and buzzer will next sound together, we need to find the least common multiple (LCM) of their ringing intervals: 10 minutes for the bell and 15 minutes for the buzzer. The LCM of 10 and 15 is 30. This means they will both sound together every 30 minutes. Starting at 8 a.m., adding 30 minutes gives us the next time they will go off together at 8:30 a.m. Imagine the scene: you’re enjoying your morning coffee, and suddenly, at 8 a.m., the bell rings, followed by the buzzer! Fast forward to 8:30 a.m., and there they go again, making sure you’re fully awake!