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# A family is moving and has a number of electronic devices in the same packing crate. One of the devic

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 3:00 pm, what time will it be when they all beep together next?

### 1 Answer by Expert Tutors

Sarah F. | Patient Physics, Math, Chemistry, and ACT/SAT TutorPatient Physics, Math, Chemistry, and AC...
4.8 4.8 (6 lesson ratings) (6)
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First, you need to find the Least Common Multiple of all of 8, 10, and 12. It is 120. To convert the 120 minutes to hours, divide by 60, which yeilds 2. So, the next time all the devices beep together will be 2 hours later, or 5:00 PM.

Hi Jennifer,

The answer we have from Sarah is very good. In case you wonder - how do I find the Least Common Multiple - let me explain that part. First, we need to factor each of the three numbers (8, 10, 12). We need the prime factors; that is, factor the number down to its prime number components. We have -

8 = 2 * 4 = 2 * 2 * 2
10 = 2 * 5
12 = 3 * 4 = 3 * 2 * 2

Next, we select the component prime numbers, starting with all of the components of the first number (8), and then the missing components from the others. So, we start with the 2 * 2 * 2 components of 8; from 10 = 2 * 5, we already have a 2, so we add the 5 component; from 12 = 3 * 2 * 2, we already have the two 2's, so we add the 3 component. In total, we have these components -

2 * 2 * 2 * 5 * 3, which is 120

Our answer is therefore 120, just what Sarah gave us.