The distribution coefficients of Ni and Zn to the Cu site in $La_{2-x}Sr_{x}CuO_{4}$(LCO) were investigated to determine the suitable solvent composition ofr crystal growth of $La_{2}{Cu}_{1-x}{M}_{x}{O}_{4}$(M=NI, Zn)(LCMO), and were found to be 4.2 for NI and 0.66 for Zn, respectively. Single crystals of LCO, and LCMO of high homogeneity were grown by traveling solvent floating zone technique using suitable solvents. NO diamagnetic signals were observed for all substituted crystals. This fact suggests that crystals of LCO partially substituted by Ni or Zn are useful as substrate crystals.