6. Find the minimum value of the expression $\left[\frac{7(a+b)}{c}\right]+\left[\frac{7(a+c)}{b}\right]+\left[\frac{7(b+c)}{a}\right]$, where $a, b$ and $c$ are arbitrary natural numbers.
Answer: 40. Evaluation: the sum of the fractions under the integer parts is no less than $14 \cdot 3=42$ (we add three inequalities of the form $7(a / b+b / a) \geqslant 14$, and each integer part is greater than the fraction reduced by 1. Therefore, the desired value is greater than $42-3=39$, i.e., not less than 40. Example: 99, 100, 100.