Length=20, depth=12, height=15.
This is easily solved with a little simple algebra. If we call the three sides A, B, and C we have:
A x B = 240
A x C = 300
B x C = 180
Multiplying these together we get:
A2 x B2 x C2 = 12,960,000
Which means that:
A x B x C = 3600
Substituting A x B = 240 back in gives C = 15 and the rest follow. QED.