An algebra problem by el amine regragui

Algebra Level 3

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

Let \(a,b\) and \(c\) be positive numbers. Find the minimum value of the expression above.

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