Question

four bells rings at intervals of 8 , 10 , 12 , 14 minutes respectively. at what time will they again ring together if they rang at 7 a.m.?​

Answer 1

The four bells ring together again at 9 pm

Solution:

Given that,

Four bells rings at intervals of 8 , 10 , 12 , 14 minutes respectively

Find LCM of 8, 10, 12 and 14

List all prime factors for each number.

Prime Factorization of 8 is:  2 x 2 x 2

Prime Factorization of 10 is:  2 x 5

Prime Factorization of 12 is:  2 x 2 x 3

Prime Factorization of 14 is:  2 x 7

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 3, 5, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 3 x 5 x 7 = 840

Thus the four rings will together at 840 minutes

1 hour = 60 minutes

Thus,

840 minutes = 14 hours

They rang at 7 a.m

They will ring together again at = 7 am + 14 hours = 9 pm

Thus they ring together again at 9 pm

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Answer 2

Answer:

the four bells will rang together at 9pm

Step-by-step explanation:

find the LCM of 8,10,12 and 14

=2×2×2×3×5×7 = 840 minutes

840 minutes = 60 ÷ 840=14 hours

7am + 14 hours = 9am