The length, breadth and height of a room are $825 \mathrm{cm}, 675 \mathrm{cm} \text{and} 450 \mathrm{cm}$ respectively. Find the longest tape which can measure the three dimensions of the room exactly.

The traffic lights at three different road crossings change after every $48$ seconds, $72$ seconds and $108$ seconds respectively. If they change simultaneously at $7 \mathrm{a}.\mathrm{m}.$, at what time will they change simultaneously again?