Question

Question 6

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

The least common multiple (LCM) of $2$ or more numbers is the smallest number that they all divide evenly.
So, lets find the LCM of given numbers:
$\begin{array}{cc}2& 48,72,108\\ 2& 24,36,54\\ 2& 12,18,27\\ 2& 6,9,27\\ 3& 3,9,27\\ 3& 1,3,9\\ 3& 1,1,3\\ & 1,1,1\end{array}$
LCM of $48,72,108=2\times 2\times 2\times 2\times 3\times 3\times 3=432$ sec.
After $432$ seconds, the lights change simultaneously.
$432$ seconds$=420+12=7\times 60+12=7$ minutes $12$ seconds. [Since, $1$ minute $=60$ seconds]
Therefore the time $=7$ a.m. $+7$ minutes $12$ seconds $=7:07:12$ a.m.