Question

Three cleaners, A, B, and C are cleaning the windows of abuilding. Person A cleans a window every 8 min, person Bevery 12 min and person C every 14 min. If they start cleaningthree windows at the same time at 14:15, at what time will startcleaning windows at the same time again? Give your answer ina 24-hour clock format, such as 19:00.

Answer 1

`\begin{gathered} \text{Get the LCM of the three persons} \\ \text{LCM}(8,12,14) \\ \text{Prime factorization of numbers} \\ 8=2*2*2 \\ 12=2*2*3 \\ 14=2*7 \\ \text{LCM}(8,12,14)=2*2*2*3*7 \\ \text{LCM}(8,12,14)=168 \\ \text{Therefore, they will start cleaning windows at the same time by every 168th minute} \\ \text{Convert it to hours + minutes} \\ 168\text{ min}=120\text{ min + }48\text{ min} \\ 168\text{ min}=2\text{ hours and 48 mins} \\ \text{Add it to 14:15} \\ 14+2=16\text{ hour} \\ 15+48=63\rightarrow1\text{ hour and 3 minutes, (add 1 hour to 16 hour and we have)} \\ \text{They will start cleaning the windows at the same time again at 17:03} \end{gathered}`