Word problem

Question

Three dogs barked at exactly 11 p.m. thereafter, fritzie barked every 4 minuets, spike barked every 5 minuets, and dixie barked every 3 minuets. What was the next time when the dogs barked at the same time?

Answer 1

To solve this problem, you must find the LCM (Least Common Multiple) of 4, 5, and 3.

 

You may (1) list the multiples of 4,5, and 3, and select the least value in all three lists:

   multiples of 4:     4  8  12  16  20   24   28  32   36   40   44   48   52   56   60   

   multiples of 5:     5   10   15   20   25   30   35   40   45   50   55   60   

   multiples of 3:     3   6   9   12   15   18   21   24   27   30   33   36   39   42   45   48   51   54   57   60

or (2) create  a group of the minimum common prime factors:

    prime factors of 4:             2   *   2

    prime factors of 5:                5

    prime factors of 3:                 3

  Minimum prime factors to include all three numbers:    2  *  2  *  3   *   5   = 60

 

60 minutes after exactly 11 p.m. is exactly midnight.  That's the next (least) time that all three dogs will bark together (common).

Answer 2

In this case we have to find out LCM of 4,5,3

 

LCM of 4,5,3 is = 60

 

so after 60 minutes they barked same time.

So at 11 pm + 1hr = 12 am they will barked same time