It is conjectured by Frankl and Furedi that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform hypergraphs with $m$ edges in cite{FF}. Motzkin and Straus theorem confirms this conjecture when $r=2$. For $r=3$, it is shown by Talbot in cite{T} that this conjecture is true when $m$ is in certain ranges. In this paper, we explore the connection between the clique number and Lagrangians for $r$-uniform hypergraphs. As an implication of this connection, we prove that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform graphs with $t$ vertices and $m$ edges satisfying ${t-1choose r}leq m leq {t-1choose r}+ {t-2choose r-1}-[(2r-6)times2^{r-1}+2^{r-3}+(r-4)(2r-7)-1]({t-2choose r-2}-1)$ for $rgeq 4.$
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