Ans; After 83 days i.e. on 84th days
Barb, Shelley, and Darcy are college roommates.
Barb goes to the library every 6 days,
Shelley goes the library every 7 days, and
Darcy goes to the library every 4 days.
If all three of them went to the library today, then the next time that they will all be at the library on the same day will be the LCM of 6,7, and 4 i.e.on 84th day.