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5:00 pm, assuming you mean all three beep at the same time.

You can solve it using the roots, but the easiest way to think about it is this:

Since 10 is one of the three numbers, then the result must be divisible by 10. Now take 12 and fine the next time it is divisible by 10... which is in 60 minutes. Is 60 also evenly divisible by 8? No! So, try the next number time that 12 and 10 match, (another 60 minutes) which is 120 minutes. Can 8 divide into 120 evenly? Yes, 15 times. Therefore in 120 minutes, or two hours, they will sync up. In fact they sync up every two hours or every odd hour if you prefer.

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Q: A divice beeps at 8 minutes 10minutes and 12 minutes if they all beep together at 3pm what time will they beep next?
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