Find The Minimum Value of the quantity Find the minimum value of the quantity $$\frac{(a^2+3a+1)(b^2+3b+1)(c^2+3c+1)}{abc}$$,where $$a,b,c>0$$ and $$ a,b,c\in R $$are positive real numbers.

$\dfrac{a^2 + 3a + 1}{a} = a + \dfrac{1}{a} + 3 \geq 2 + 3 = 5$ by AM-GM. So $LHS \geq 5^3 = 125$ with equality at $  a = b = c = 1$
