Let $a, b$ and $c$ be natural numbers. Determine the smallest value that the following expression can take: $$\frac{a}{gcd\,\,(a + b, a - c)} + \frac{b}{gcd\,\,(b + c, b - a)} + \frac{c}{gcd\,\,(c + a, c - b)}.$$. Remark: $gcd \,\, (6, 0) = 6$ and $gcd\,\,(3, -6) = 3$.