Three bells are ringing continuously at intervals of $30,40and45$minutes respectively. At what time will they ring together if they ring simultaneously at $5$A.M.?

Calculate the LCM of $30,40and45$

$$\begin{gathered} 30=2\times 3\times 5 \\ 40=2\times 2\times 2\times 5 \\ 45=3\times 3\times 5 \end{gathered}$$

LCM of $30,40and45$= $2\times 2\times 2\times 3\times 3\times 5=360$

After $360minutes=360÷60=6hours$ they will ring together.

it means $5+6=11$AM .

Hence at $11$AM three bells will rang together.