Given that $\operatorname{HCF}(306,657)=9$, find $\operatorname{LCM}(306,657)$.

Solution:

$\operatorname{LCM}(306,657)$

$=\frac{\mathbf{3 0 6} \times \mathbf{6 5 7}}{\mathbf{H C F}(\mathbf{3 0 6}, \mathbf{6 5 7})}=\frac{\mathbf{3 0 6} \times \mathbf{6 5 7}}{\mathbf{9}}=22338$