This is a hint, not an answer :)
let them work together:
after 1 day - A does 1/15 of the work, and B does 1/24 of the work.
after 2 days - A does 2/15 of the work and B does 2/24 of the work.
after 3 days - A: 3/15 of the work, B: 3/24 of the work
after 4 days - A= 3/15, B=4/18
after 5 days - A=4/15, B=5/18
etc.
we need to find on what day do they do a 1/1 of the work together.
for that we need a "Lowest Common Denominator".
