The Product is 2016, But Minimize the Sum

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

first of all $2016=2^5×3^2×7$ we must have to choose three numbers whose sum is minimum so these numbers must be close to each other to give minimum value , I got these numbers as $12,12,14$ which upon adding gives $\boxed{38}$ which was already their in options so I got help from options as well :-)

2016=4×504=4×4×126=4×4×14×9= 4×4×14×3×3=12×12×14. To see the sum minimum the nubers must be as close as possible to each other. So 12+12+14=38.