jmc

Since $$j=\frac{24}{k}=\frac{48}{l}$$we have $l=2k$. So $18=2k^2$, which means that $9=k^2$. Since $k$ has to be positive, this implies that $k=3$. This means that $j=8$, and $l=6$. Hence $j+k+l=\boxed{17}$.

OR

Take the product of the equations to get $jk\cdot jl\cdot kl=24\cdot 48\cdot 18$. Thus $$(jkl{)}^2=20736.$$So $(jkl{)}^2=(144{)}^2$, and we have $jkl=144$. Therefore, $$j=\frac{jkl}{kl}=\frac{144}{18}=8.$$From this it follows that $k=3$ and $l=6$, so the sum is $8+3+6=\boxed{17}$.