Question

three bells ring at intervals of 12, 15 and 18 seconds respectively if they started ringing together at 8:35 a.m. at what time will they together again after the earliest

Answer 1

Solutions :-

Given :
Three bells ring at intervals of 12, 15 and 18 seconds respectively.


Taking the LCM of 12, 15 and 18 :-
12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180
15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180
18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, 180

180 is common in 12, 15 and 18. Therefore, LCM of 12, 15 and 18 is 180.


Given : They started ringing together at 8:35 a.m.

Second time they ringing together = 8:35 + 180 seconds = 8:35 + 3 minutes = 8.38 a.m.


Hence,
Second time they ringing together at 8:38 a.m.

Answer 2

Question :

Three bells ring at intervals of 12, 15 and 18 seconds respectively if they started ringing together at 8:35 a.m. at what time will they together again after the earliest.

Answer:

$\huge{\boxed{\boxed{\red{8 : 38\:am}}}}$

Step-by-step explanation:

Given

Three bells ring at intervals of 12, 15 and 18 seconds .

Find the L.C.M

12 = 3 × 2 × 2

15 = 3 × 5

18 = 3 × 2 × 3

L.C.M = 3 × 3 × 2 × 2 × 5

⇒ L.C.M = 9 × 20

⇒ L.C.M = 180

Convert to minutes

L.C.M = 180 s

60 s = 1 min

180 s = 3 min

Hence after 3 minutes they will ring together again .

Add the minutes

8 : 35 + 3

= 8 : 38

The time will be 8 : 38 am .