The dimensions of a gift box are consecutive positive integers such that the height is the least integer and the length is the greatest integer. If the height is increased by 1cm, the width is increased by 2cm, and the length is increased by 3cm, then a larger box is constructed such that the volume is increased by 456cm3. determine the dimensions of each box.
and so far I got to
.___. then I got stuck >< I don't even know if I'm on the right track.
According to the answers in the back, the dimensions of the first box are
9cm by 8cm by 7cm
the second box would be
12cm by 10cm by 8cm
Thank you in advance for your help ^^