Question

The traffic lights at three different road crossings change after every $48$ seconds, $72$ seconds and $108$ seconds. If they start changing simultaneously, at $10$ a.m., after how much time will they change again simultaneously?

• A. $6$ mins $18$ secs
• B. $8$ mins $10$ secs
• C. $7$ mins $12$ secs
• D. $7$ mins $8$ secs

Answer 1

The correct option is C $7$ mins $12$ secs

Traffic Lights change after $48$, $72$, $108$ seconds.

We need to find out the LCM of $48,72,108$ in order to find the time when they change simultaneously.

$48$ $\to$ $2$$\times$$2$$\times$$2$$\times$$2$$\times$$\times$$3$

$72$ $\to$ $2$$\times$$2$$\times$$2$$\times$$3$$\times$$3$

$108$ $\to$ $2$$\times$$2$$\times$$3$$\times$$3$$\times$$3$

L.C.M. of $48,72,108$$\to$ $2$$\times$$2$$\times$$2$$\times$$2$$\times$$3$$\times$$3$$\times$$3$ $\to$ $432$

They will change after $432$ seconds.

$432$ seconds $\to$ $7$ minutes $12$ seconds

Hence, option C is correct.