Question

the traffic lights at three different road crossing change after every 48 seconds 72 second hand 108 seconds respectively if they changed simultaneously
at 7 am what time will they simultaneous again

Answer 1

take the lcm of time then they will be simult
that is lcm of 48 s,72s,108s = 5616 sec = 1 hr 33 min 36 sec
if thay start at 7 AM they will be simultaneous at 8.33.36 AM

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