josie takes 5 min to run a lap, bob takes 6 min to run a lap, and karen takes 8 min to run a lap. When will jose and bob again meet at the starting place?

Question

josie takes 5 min to run a lap, bob takes 6 min to run a lap, and karen takes 8 min to run a lap. When will jose and bob again meet at the starting place?

When will Bob and Karen again meet at the starting place?

When will Josie, bob and Karen again meet at the starting place?

Answer 1

Josie is at the starting place at times:    0    5    10    15    20    25    30    35    40

Bob is there at times:                           0    6    12    18    24    30    36    42    48

Karen is there at times:                        0    8    16    24    32    40    48    56    64

 

Josie and Bob start at time=0 and meet at the Start again at time=30.  This is the Least Common Multiple (LCM) of 5 and 6.

Bob and Karen start at time=0 and meet at the Start again at time=24, the LCM of 6 and 8.

Josie, Bob and Karen start at time=0 and meet again at time=120, the LCM of 5,6 and 8.

 

Now, you could extend the lists and select the first common number (that is, the LCM) or you could list the prime factors.  For example, the LCM of 5, 6 and 8:

   5:     5

   6:     2*3

   8:     2*2*2

 

The LCM has enough factors that 5, 6 and 8 are factors of the LCM.  That is, 2*2*2*3*5 = 120.