The traffic lights at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8 hours, then at what time will they again change simultaneously?

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Solution

The traffic lights at three different places changes after every 48 seconds, 72 seconds and 108 seconds, respectively.
∴ Interval of change = LCM (48, 72, 108)
Prime factorisation:
48 = $2^{4} \times 3$
72 = $2^{3} \times 3^{2}$
108 = $2^{2} \times 3^{3}$
LCM = Product of greatest power of each prime factor involved in the numbers
= $2^{4} \times 3^{3} = 432$ seconds = 7 min 12 seconds [∵ 1 min = 60 seconds]
∴ Required next time of simultaneous change = 8 : 7 : 12 hours

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