10. Four bells ring at intervals of 8, 10, 12 and 14 minutes respectively. At what time will they
together if they rang together at 7 a.m.?
Answers
Answer: 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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