Question

The traffic light at three different road crossings change after every 48 sec, 72 sec 108 respectively . If they all change simultaneously at 8.20 hrs, when will they again change simultaneously ?

Answer 1

AnswEr :

Traffic Lights Change after 48 sec, 72 sec and 108 sec respectively. They Changed Together at 08 : 20 : 00 AM.

• We will first calculate LCM of Times :

➟ 48 = 2 × 2 × 2 × 2 × 3

➟ 72 = 2 × 2 × 2 × 3 × 3

➟ 108 = 2 × 2 × 3 × 3 × 3

⠀

$\Rightarrow\sf{LCM(48, 72, 108)=2\times2 \times2\times2\times3\times3\times3}$

⇒ LCM(48, 72, 108) = 432 seconds

⇒ LCM(48, 72, 108) = 432 / 60 minutes

⇒ LCM(48, 72, 108) = 7 min. 12 sec.

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• Traffic Lights will Change Together Again:

⇝ Last Time + LCM Of Time

⇝ (08 : 20 : 00 AM) + (7 min. 12 sec)

⇝ 08 : 27 : 12 AM

∴ They'll again change at 08 : 27 : 12 AM.

Answer 2

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If the traffic lights change simultaneously at 8 : 20 a.m, then they will change simultaneously again after the LCM of the duration i.e. 48 s, 72 s and 108 s.

LCM of these durations by prime factorisation

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

108 = 2 × 2 × 3 × 3 × 3 = 2² × 3³

LCM of 48, 72 and 108 is 2⁴ × 3³ = 432 seconds.

Hence, They will change after 432 seconds i.e. 7 minutes 12 seconds.

The traffic lights will change after:

8 am + 27 minutes 12 seconds

08 : 27 : 12 am