Four bells ring at intervals 6,8,12,20 minutes.they ring simultaneously at 8a.m. at what time they will ring together
Answers
Thus the bells will ring simultaneously after 120 mins.
Thus after 8 am they will ring at 10 am.
At 10 am the four bells will ring together
Solution:
Given that,
Four bells ring at intervals 6, 8, 12, 20 minutes
They ring simultaneously at 8 a.m
Find the LCM of 6, 8, 12, 20
List all prime factors for each number
Prime Factorization of 6 is: 2 x 3
Prime Factorization of 8 is: 2 x 2 x 2
Prime Factorization of 12 is: 2 x 2 x 3
Prime Factorization of 20 is: 2 x 2 x 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 3 x 5 = 120
After, 120 minutes the bell will ring together
60 minutes = 1 hours
120 minutes = 2 hours
At what time they will ring together ?
8 am + 2 hours = 10 am
Thus, at 10 am the four bells will ring together
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