At a certain factory, each of Machines \((A, B,\) and \(C\) is periodically on for exactly \(1\) minute and periodically off for a fixed number of consecutive minutes. The table above shows that Machine \(A\) is on and uses \(15\) units of power every \(18th\) minute, Machine \(B\) is on and uses \(18\) units of power every \(15th\) minute, and Machine \(C\) is on and uses \(12\) units of power every \(12th\) minute. The factory has a backup generator that operates only when the total power usage of the \(3\) machines exceeds \(30\) units of power. What is the time interval, in minutes, between consecutive times the backup generator begins to operate?

A. 36
B. 63
C. 90
D. 180
E. 270

Answer: C

Source: Official Guide