MHB Solving 2 Watches with 12 Hour Cycle Problem

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Two watches with a 12-hour cycle have different timekeeping issues: one gains 2 minutes daily while the other loses 3 minutes. To determine when they will next show the correct time together, calculations reveal that Watch 1 takes 360 days to reset, and Watch 2 takes 240 days. The least common multiple (LCM) of these two periods is 720 days. Therefore, both watches will next display the correct time together after 720 days. The solution is confirmed as correct.
Marcelo Arevalo
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Can you help me please on these problem.

"I have 2 watches with a 12 hour cycle. One gains 2 minutes a day and the other loses 3 minutes a day. If I set them at the correct time, how many days will it be before they next together tell the correct time? "my idea of solving it is using LCM, bu t I can't get my thoughts to come together. please, kindly help.
thank you.
 
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Marcelo Arevalo said:
Can you help me please on these problem.

"I have 2 watches with a 12 hour cycle. One gains 2 minutes a day and the other loses 3 minutes a day. If I set them at the correct time, how many days will it be before they next together tell the correct time? "my idea of solving it is using LCM, bu t I can't get my thoughts to come together. please, kindly help.
thank you.

I think you're on the right track here. Why don't you calculate how many days each watch would take to be correct again on their own? So, Watch 1 on its own takes how many days to be correct again? Watch 2 on its own takes how many days to be correct again? That might suggest something to you.
 
Watch 1 takes about 360 days to tell correct time again
Watch 2 takes about 240 days to tell correct time again

getting the LCM of both watches ; together they need 720 days for both to tell correct time.

Is it correct??
answer is 720 days.
 
Yes, it is correct.
 

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