Question

The 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

The traffic light at three different road crossing change after every 48seconds,72seconds and 108seconds respectively

So,

48=2×2×2×2×3

72=2×2×2×3×3

108=2×2×3×3×3

Therefore, L.CM of 48,72,108 is

(2×2×2×2×3×3×3)

=432

So, time when they change again =432seconds

But we need to find time after 7am So, first we convert 432seconds into minutes.

Time=432seconds=(432/60) minutes

∴Time=7 minutes12 seconds

Thus,

Required time =7am+7minutes 12seconds

=7:07:12am

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