Of the goose eggs laid at a certain pond, ~$\frac{2}{3}$~ hatched, and ~$\frac{3}{4}$~ of the geese that hatched from those eggs survived the first month.  Of the geese that survived the first month, ~$\frac{3}{5}$~ did not survive the first year.  If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?