Answer to Question #128986 in Discrete Mathematics for Fatih

Question

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?

Answer 1

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.