Using first-principles calculations with ultrasoft pseudopotential formalism and the generalized gradient approximation for the exchange-correlation functional, we study the stability of MonSm (n =1-6 and m ranging from n to 3n) clusters and obtain the optimal stoichiometry for each n corresponding to the magic cluster. It is found that in this size range, the lowest-energy structures favor a core of metal atoms, which is covered by sulfur. In particular, we observe that for Mo6S14 isolated clusters, a 3D structure is significantly lower in energy as compared to platelet structures found recently on Au (111) surface. The composition ratio between S and Mo in the magic clusters is less than 2 for n=3 and greater than 2 for n<3. The structural stability of the magic clusters arises from the optimization of the Mo-Mo and Mo- S bonding as well as the symmetry of the cluster. Addition of a terminal sulfur in a magic cluster generally lowers its binding energy. The presence of partially occupied d-orbitals in Mo atoms contributes to Mo-Mo bonding and for higher S concentration it leads to sulfur-sulfur bond formation. The variation in energy due to a change in the sulfur composition suggests that sulfurization of the magic clusters is generally more favorable than desulfurization.