6 . Find all positive integers $a, b$ such that
$$(a, b)+9[a, b]+9(a+b)=7 a b .$$
6. Let $(a, b)=d, a=d x, b=d y$, then $(x, y)=1$. Substituting into the condition, we get
$$1+9 x y+9(x+y)=7 d x y$$

Thus, $\square$
$$9<7 d=9+9\left(\frac{1}{x}+\frac{1}{y}\right)+\frac{1}{x y} \leqslant 9+9 \times 2+1=28 \text {. }$$

From this, we know that $d=2,3$ or 4. Substituting these values into the indeterminate equation for $x, y$, we can find that $(a, b)=(4,4),(4,38)$ or $(38,4)$.