Question

the traffic lights at the three different roads crossings change after every 36 seconds ,48 seconds,72 seconds if they change simultaneously at 9 a.m. at what time will they change together next​

Answer 1

Answer:

They will meet together at starting point after,

LCM of (54,42,63) seconds

54=2×3×3×3

42=2×3×7

63=3×3×7

Required LCM =3×3×3×2×7=378 seconds =6.3 minutes.

Answer 2

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If the traffic lights change simultaneously at 9 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:

9 am + 7 minutes 12 seconds

09 : 07 : 12 am