  For a Kac-Moody algebra $\mathfrak{g}$ of rank $2$ and a fundamental weight
$\lambda$, we explicitly give an isomorphism between the set of
Lakshmibai-Seshadri paths $\mathbb{B}(\lambda)$ and monomial realization
$\mathcal{M}(\lambda)$. As an application, we also give an explicit form of
monomial realization $\mathcal{M}(\lambda)$ in terms of Weyl groups.
