  In this paper, we prove the identity $$\lcm\{\binom{k}{0}, \binom{k}{1},
>..., \binom{k}{k}\} = \frac{\lcm(1, 2, ..., k, k + 1)}{k + 1} (\forall k \in
\mathbb{N}) .$$
  As an application, we give an easily proof of the well-known nontrivial lower
bound $\lcm(1, 2, ..., k) \geq 2^{k - 1}$ $(\forall k \geq 1)$.
