Question

traffic lights at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively . if they change simultaneously at 7:am,at what time will they change simultaneously again?​

Answer 1

Answer:

let us take the LCM of the given time that is 48 seconds, 72 seconds, 108 seconds

⇒ 48 = 2 × 2 × 2 × 2 × 3

⇒ 72 = 2 × 2 × 2 × 3 × 3

⇒ 108 = 2 × 2 × 3 × 3 × 3

LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)

= 432

So after 432 seconds they will change simultaneously

60 seconds = 1 minute

on dividing 432 / 60 we get 7 as quotient and 12 as reminder

432 seconds = 7 min 12 seconds

therefore, The time = 7 a.m. + 7 minutes 12 seconds

the lights change simultaneously at 7:07:12 a.m

i hope this helps you

Answer 2

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If the traffic lights change simultaneously at 8 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 + 7 minutes 12 seconds
• 08 : 07 : 12 am