How many ordered triples $\left(x,y,z\right)$ of positive integers satisfy $lcm\left(x,y\right)=72, lcm\left(x,z\right)=600$ and $lcm\left(y,z\right)=900?$

The number $2013$ is expressed in the form $2013=\frac{\left(a_1!\right)\left(a_2!\right)\dots \left(a_m!\right)}{\left(b_1!\right)\left(b_2!\right)\dots \left(b_n!\right)}$

where $a_1\ge a_2\ge \dots \ge a_m$ and $b_1\ge b_2\ge \dots b_n$ are positive integers and $a_1+b_1$ is as small as possible. What is
$\left|a_1-b_1\right|?$