Finding product of three numbers given respective products

Question

While solving a problem about volumes of parallelepipeds, I came across three expressions involving the products of its respective sides: $a,b$ and $c$. The equations are the following:

$ab = 60$

$ac = 40$

$bc = 24$

Now I want to find the volume of the parallelepiped $V=abc$. Is there an elegant way to do so from these equations? Thank you in advance.

Answer 1

Multiply all three equations together and take the square root of both sides of the resulting equation.

Answer 2

Hint: Letting $x=\frac{20}a$, the first two equations give that $b=3x$ and $c=2x$, putting this into the third one: $6x^2=24$.