An algebra problem about minimum value

Algebra Level 3

(a+1)(b+1)(c+1)(1a+1)(1b+1)(1c+1) (a + 1)(b+ 1)(c+ 1) \left(\dfrac1a + 1\right)\left(\dfrac1b + 1\right)\left(\dfrac1c + 1\right)

Let a,ba,b and cc be positive numbers. Find the minimum value of the expression above.

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