smc

Draw diagram as shown, where $P$ and $Q$ are on the same side. Let $AP=x$ and $QB=y$. Since $P$ divides $AB$ in the ratio $2:3$, $\frac{x}{y+2}=\frac{2}{3}$. Since $Q$ divides $AB$ in the ratio $3:4$, $\frac{x+2}{y}=\frac{3}{4}$. Cross multiply to get a system of equations. $$3x=2y+4$$ $$4x+8=3y$$ Solve the system to get $x=28$ and $y=40$. Thus, $AB=40+28+2=70$, so the answer is $\boxed{70}$.