The length, breadth and height of a room are \(12\) \(m\) and \(25\) \(cm\), \(8\) \(m\) and \(50\) \(cm\) and \(10\) \(m\) and \(25\) \(cm\), respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
 
Ans: \(cm\)