In this paper, we investigate the first few largest coset leaders modulo $\frac{q^m+1}λ$ where $λ\mid q+1$ and $q$ is an odd prime power, and give the dimensions of some LCD BCH codes of length $\frac{q^m+1}λ$ with large designed distances.We also determine the dimensions of some LCD BCH codes of length $n=\frac{(q^m+1)}λ$ with designed distances $2\leq δ\leq \frac{ q^{\lfloor(m+1)/2\rfloor}}λ+1$, where $ λ\mid q+1$ and $1<λ<q+1$. The LCD BCH codes presented in this paper have a sharper lower bound on the minimum distance than the BCH bound.