If there are 4 ships at a port and the first one leaves and comes back every three weeks, the second one every nine weeks, the third one every 12 weeks, and the fourth every 24 weeks when will they all be in the port at the same time/when will they be there all at the same week

After 72 weeks they will be in the port at the same time.

Step-by-step explanation:

Given, Total ships = 4

The first one leaves and comes back every 3 weeks, the second one every 9 weeks, the third one every 12 weeks, and the fourth every 24 weeks .

So, the number of weeks they will take to  be in  the port at the same time = L.C.M. (3, 9, 12 , 24)   (L.C.M. = least common multiple)

Since, 9= 3 x 3

12 = 2 x2 x 3

24 = 2 x 2x 2 x3

then, L.C.M. (3, 9, 12 , 24)= 2 x 2x 2 x 3 x3 =72

Hence after 72 weeks they will be in the port at the same time.