Question

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 a.m., at what time will they change simultaneously again?

Answer 1

$\text{L.C.M of 48, 72, 108 = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 432 sec.}$



$\text{After 432 seconds the lights changed}$$\text{simultaneously.}$



$\text{432 second = 7 minutes 12 seconds}$



$\textbf{Therefore the time = 7 a.m + 7 minutes 12 secs.}$
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \textbf{ = 7:07:12 a.m}$

Answer 2

Answer:

Time at which they will change simultaneously again= LCM of 48, 72 and 108

LCM= 2×2×2×2×3×3×3

= 4×4×9×3 = 432

So, after 432 seconds they will chane simultaneously.

432 seconds= 7 minutes 12 seconds

The time when they will change simultaneously again= 7 a.m. + 7 min + 12 secs. = 7:08:12 a.m.