Question

the traffic lights at three different road crossing change after 72 sec , 108sec. ,132 sec respectively . if they change simultaneously at 7 am. at what time they change again simultaneously ​

Answer 1

Given : traffic lights changes after

i).72 sec.ii).108 sec..iii).132 sec..

Now,

they blink together at 7 a.m.

Here we need to find the LCM

of 72 and 108 and 132

=》 72=2×2×2×3×3

=》108=2×2×3×3×3

=》132=2×2×3×11

LCM =product of prime factors

with highest power

=> 2×2×2×3×3×3×11

=>2376 seconds

Also,

2396 sec.= 2396/60 minutes

=39.6

Ans: They blink together at

7hours 39minutes 6seconds.

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