Question

The traffic lights at three different
road crossings charge after every 50 seconds and 72 seconds respectively if they change
simultaneously at 8:15am at
What time will they change
simultaneously again ​

Answer 1

take lcm of 50 ,72

is 1800 seconds is equal to 0.5 hrs

so 8:15 +0.5

9:05 am they will change again

Answer 2

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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