please help

Question

Barb, Shelley, and Darcy are college roommates. Barb goes to the library every 8 days, Shelley goes the library every 5 days, and Darcy goes to the library every 12 days. If all three of them went to the library today, when is the next time that they will all be at the library on the same day?
a) 480 days from now
b) 40 days from now
c) 96 days from now
d) 120 days from now
e) 60 days from now
f) None of the above.

Answer 1

find the least common multiple of 8, 5, and 12

8=2*2*2

5=5

12=2*2*3

LCM=2*2*2*5*3=120 days d)

or,...

8,16,24,32,40,48,56,64,72,80,88,96,104,112,120

5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120

12,24,36,48,60,72,84,96,108,120