jmc

Subtract 4609 from both sides of the congruence to obtain $x\equiv -2505(\mathrm{mod}12)$. By dividing 2505 by 12, we find that the least integer $k$ for which $-2505+12k>0$ is $k=209$. Adding $12\cdot 209$ to $-2505$, we find that $x\equiv 3(\mathrm{mod}12)$. Thus $\boxed{3}$ is the least integer satisfying the given congruence.