The traffic lights at three different road crossings change after every 48 seconds, 72 second and 108 seconds respectively . If they change simultaneously at 7 a.m., at what time will they change simultaneously again ?
Answers
Given :-
The traffic lights at three different road crossings change after every 48 seconds, 72 second and 108 seconds respectively . If they change simultaneously at 7 a.m
To Find :-
At what time will they change simultaneously again ?
Solution :-
At first we need to find LCM of 48,72 and 108
Factor of 48 = 2 × 2 × 2 × 2 × 3
Factor of 72 = 2 × 2 × 2 × 3 × 3
Factor of 108 = 2 × 2 × 3 × 3 × 3
LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3
LCM = 432 sec
1 min = 60 sec
432 sec = 432/60 = 7 min 12 sec
Therefore
It will rang after 7 : 7 : 12 am
Answer: 7 minutes 12 seconds past 7 a.m.
Step by step explanation:
LCM of 48 seconds, 72 seconds and 108 seconds.
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
Now,
So, divide 432 by 60...
We will get 7.2 seconds..
Now,
1 minute = 60 seconds
So, 7 minutes = 7×60 seconds= 420 seconds.
Now, Subtract 432 and 420...
= 4 3 2
- 4 2 0
0 1 2
☆Hence, 432= 7 minutes 12 seconds...
So, at 7 minutes 12 seconds past 7 a.m., they will change simultaneously again...
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