Four bells ring at intervals of $6,7,8$ and $9$ seconds respectively. After how many seconds do all the bells ring together?

The correct options are A : $504$

In order to find the time at which all the bells ring together, we should find out the LCM of $6,7,8$ and $9.$

The LCM of the given numbers can be found as follows:

$\begin{array}{cc}2& 6,7,8,9\\ 3& 3,7,4,9\\ & 1,7,4,3\end{array}$

$\therefore$ LCM $=2\times 3\times 1\times 7\times 4\times 3=504$

Therefore, the four bells ring together after $504$ seconds and at multiples of $504$ seconds.