"The least common multiple (LCM) is the smallest number which is a multiple of two numbers. If two numbers have no common factors greater than 1, then their LCM will be their product. For example, take numbers 7 and 9. They have none common factor greater than 1."
Answer: 
Step-by-step explanation:
For this exercise you need to apply the Pythagorean Theorem. This is:

Where "h" is the hypotenuse of the Right triangle and "l" and "m" are the legs.
In this case, you can identify that:

Knowing these values, you can substitute them into
:

Now you must solve for "c":

Evaluating, you get:

To simplify the result:
- Descompose 32 into its prime factors:

- By the Product of powers property, you know that:

- Make the substitution:

- Finally, knowing that
, you get:

V = 1/3 l h w
V = 1/3 (12)(15)(9)
V= = 540
answer 540 m^3