Suppose we have a finite Egyptian fraction decomposition of a rational: $$\frac{n}{m} = \sum_{i=1}^k \frac{1}{x_i}$$ such that

(i) $x_i>0$,

(ii) $x_i \neq x_j$ for $i \neq j$, and

(iii) $\gcd(m, x_1,x_2,...x_k) = 1$.

Are their any known results concerning $\max_{i,j} |x_i-x_j|$ or maybe $\max_{i,j} |\frac{x_i}{x_j}|$?

For example,

$\frac{5}{121} = \frac{1}{26} + \frac{1}{350} + \frac{1}{275275}$ or
$\frac{5}{121} = \frac{1}{33} + \frac{1}{93} + \frac{1}{3751}.$
Certainly the latter expression is "better" than the previous one for some vague notion of "better".

Note: Condition (iii) means we don't consider $\frac{5}{121}= \frac{1}{33}+\frac{1}{121}+\frac{1}{363}$ since this is really just a good decomposition of $\frac{5}{11}$ that has been divided through by $11$.

Motivation: I'm investigating a technique in my research that would produce Egyptian fraction representations where all the denominators are roughly the same size and I'm curious if this has been looked at before.