Question

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

Answer 1

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We should find out LCM of 48 ,72 and 108

prime factorization of

48÷2×2×2×2×3

72=2×2×2××3×3

108=2×2×3×3×3

LCM=2×2×2×2×3×3×3=432

432/60=7.2 min

therefore 7:00am+7.2 min

The required time is 7:07:02 am

Answer 2

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Deja vu (°_o)

If the traffic lights change simultaneously at 7 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:

• 7 am + 7 minutes 12 seconds
• 07 : 07 : 12 am