This is related to the question If a finite set of rational numbers sums to one, does one of the rationals have a denominator equal to the LCM of all the denominators?
Suppose $1 = \sum\limits_{i=1}^n \frac{p_i}{q_i}$, where $p_i,q_i$ are positive integers, and $\gcd(p_i,q_i)=1$.
Let $k = \max_{i=1}^n \{ q_i\}$. $m=\operatorname{lcm}(q_1,\ldots,q_n)$.
Can we bound $m$ by $k$ and $n$? The obvious bound is $m\leq k^n$; however, I feel that there exists better bounds.