Hello Vjesus12.

We know that the three lights are switched on for the first time (and at the same time) at 9:00 A.M and they change each 36, 42 and 72 seconds respectively.

We have to find the time when they all change simultaneously. To find this time, we have to find the least common multiple of 36, 42 and 72, because this will be the first time when they change simultaneously after the 9:00 A.M.

Now $$36=2\cdot2\cdot3\cdot3=2^2\cdot3^2$$ $$42=2\cdot3\cdot7$$ $$72=2\cdot2\cdot2\cdot3\cdot3=2^3\cdot3^2.$$ Now, the least common multiple is $$LCM\left(36,\ 42,\ 72\right)=2^3\cdot3^2\cdot7=8\cdot9\cdot7=504.$$ Therefore, after 504 seconds all three ligths will change simultaneously.

Now $$504\ \text{secs}\ =\ 480\text{ secs}\ +\ 24\text{ secs}=\ 8\ \min\ +\ 24\ \text{secs} \ . $$ Therefore, the three ligths will change simultaneously for the first time at 9: 08 : 24 A.M.

This implies that the correct answer is the option B.

I really hope it is clear enough. <i class="em em-wink"></i>