two alarms are set to go off in the morning. one alarm will buzz every 6 minutes and the other will beep every 9 minutes. if both alarms go off 6:15 am what is the next time the both alarms will go off at the same time

Explanation:

The LCM of 6 and 9 is 18. We can see that by listing out the multiples

multiples of 6 = {6,12,18,24,30,...}

multiples of 9 = {9,18,27,36,45...}

Or we could multiply 9*6 = 54, and divide by the GCF 3 getting 54/3 = 18. There are a few options to find the LCM.

The LCM being 18 means that every 18 minutes, both alarms will go off. If they both sound off at 6:15 AM, then the next time they trigger together is 6:33 AM since 15+18 = 33, and there is no carry over to the next hour.

You can think of the time values adding like this

6:15 + 0:18 = (6+0):(15+18) = 6:33