A family is moving and has a number of electronic devices in the same packing crate. One of the devices beeps every 8 minutes, another device beeps every 10 minutes, and a third device beeps every 12 minutes. If all the devices beeped together at 3:00pm, what time will they all beep together next?

What is the LCM for 8, 10 , and 12 ?

LCM, not GCF

Not sure, 120?

Right. So what's 120 minutes from 3:00?

first device: 8 16 24 .... 120

2nd device : 10 20 30 ... 120
3rd device: 12 24 36 ... 120

so 120 minutes from now they coincide
120 min = 2 hours

so at 5:00 all 3 will peep at the same time

thank you!

To find the next time the devices will beep together, we need to determine the least common multiple (LCM) of 8, 10, and 12.

1. Start by listing the multiples of each number:
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ...
- Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, ...
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, ...

2. Identify the first common multiple in the lists above. The least common multiple of 8, 10, and 12 is 120. This means that the devices will beep together every 120 minutes.

3. Now, determine the time elapsed since the devices beeped together at 3:00 pm. We need to convert the time to minutes, which gives us 3:00 pm = 3 * 60 = 180 minutes.

4. Finally, we add the LCM to the elapsed time to find the next time the devices will beep together:
180 minutes + 120 minutes = 300 minutes

Converting 300 minutes back to hours and minutes, we get:
300 minutes = 5 hours + 0 minutes

Therefore, the devices will beep together again at 5:00 pm.