Answer to Question #128986 in Discrete Mathematics for Fatih

Question #128986

Two fire sirens give alarms at intervals of 5/7, 7/8 hours. Since these two fire sirens sounded an alarm at 04:00 on Friday at the same time, on which day and at what time do they alarm together again?


1
Expert's answer
2020-08-10T17:39:30-0400

To determine when the two alarms will sound together again, we need to find the lest common multiple between the two intervals.

LCM"(\\frac{5}{7},\\frac{7}{8})=\\frac{LCM(5,7)}{HCF(7,8)}"

LCM(5,7) is given by



HCF(7,8) = 1


Therefore, LCM"(\\frac{5}{7},\\frac{7}{8})=\\frac{35)}{1)}" = 35

This means that the two sirens will alarm together again after 35 hours. Since they both sounded at 04:00 of Friday, we add 35 hours to this time and get, 15:00 on Saturday.




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