Question

Four bells ring at an interval of 4, 7, 12 and 14 seconds respectiv
if the four Bells begin to ring at 12 o'clock when will the next ring together and how often will they do so in the next 14 minutes.

Answer 1

To find the answer, we need to find the LCM of 4, 7, 12, 14.




First, list the prime factorization of each number. If you need help with prime factorization,



Now highlight the unique factors. Remember, highlight the factors that occur most frequently


4:2*2


7: 7


12: 2*2*3


14: 2*7


Now multiply all of the highlighted factors

2*2*3*7=84

So the LCM of 4,7, 12, and 14 is 84


This means that every 84 minutes, the four bells will ring at the same time (you start the timer when they first ring)


So because 84 min = 60 min + 24 min = 1 hr 24 min, add this to 12:00 to get
12:00 1:24 ------ 13:24

Since 13:24 is the same as 1:24 pm, this means that the four bells will ring together again at 1:24 pm