<s>[INST] Finding the smallest value of the sum 
The multiplication of three natural numbers $a$, $b$ and $c$ equals $2016$. What is the smallest value of $a + b + c$?

I started by a prime factorization to find that $2016 = 2^5 \cdot 3^2 \cdot 7$.
What should I do next?
 [/INST] If we consider the fact that $7=2\cdot3\cdot\frac76$, then $2016=2^6\cdot3^3\cdot\frac76$, and it becomes easy to represent this number as a product of $\color\red3$ natural numbers which are as close to each other as possible:


*

*$a=2^{6/\color\red3}\cdot3^{3/\color\red3}=12$

*$b=2^{6/\color\red3}\cdot3^{3/\color\red3}=12$

*$c=2^{6/\color\red3}\cdot3^{3/\color\red3}\cdot\frac76=14$

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