four bells ring at intervals of 8 and 12 and 14 minutes respectively at what time will they again ring together if the rang together at 7:00 a.m.
Answers
Answer:
the bell will ring after 840 minutes of 7 AM
Step-by-step explanation:
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.