Question

The traffic lights at three different road crossings change after every 24 seconds,
36 seconds and 72 seconds respectively. If they change simultaneously at 9pm, at what
time will they change simultaneously again?
HOTS)​

Answer 1

Step-by-step explanation:

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=432second

=

60

432

minutes

∴Time=7 minutes12 seconds

Thus,

Required time =7am+7minutes 12seconds

=7:07:12am

HOPE IT HELPS YOU... PLEASE MARK MY ANSWER AS BRAINLIEST.

Answer 2

$\large \green{ \fcolorbox{gray}{black}{ ☑ \: \textbf{Verified \: answer}}}$

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

36 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

60 = 5 × 3 × 2²

72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

LCM of 48, 72 and 108 is 2⁴ × 3³ = 360 seconds.

Hence, They will change after 360 seconds i.e. 6 minutes 12 seconds.

The traffic lights will change after:

9 am + 6 minutes

09 : 06 : 00 am