39
41
43
38
40

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You can even use AM GM inequality.

$\frac{a+b+c}{3}≥\sqrt[3]{abc}$

Given that abc=2016,

$a+b+c≥3 \times \sqrt[3]{2016}$ => $a+b+c≥3 \times 12.633$

For minimum value, $a+b+c=3 \times 12.633 =>a+b+c=37.899 ≈\boxed{38}$