$Mg(OH)_2$ particles were prepared by precipitation and a hydrothermal treatment to examine the effect of $MgCl_2$ concentration, alkali type and concentration, temperature, hydrothermal treatment on the formation of $Mg(OH)_2$ particles using full factorial design, as one of DOE (Design of experiment) methods. The primary particle size is similar to the secondary particle size for the samples after the hydrothermal treatment, where the average particle size of $Mg(OH)_2$ increased with increasing the concentration of $MgCl_2$ and hydrothermal temperature and decreasing alkali/Mg molar ratio. On the other hand, for the samples prepared from precipitation, the secondary particle size is larger than the primary particles due to aggregation. The difference in alkaline source is that the particles prepared from $NH_4OH$ exhibit the larger size with better dispersion than those from NaOH. Low density polyethylene and ethylene-co-vinyl acetate (LDPE-EVA) resin composed of the smaller secondary particle size of $Mg(OH)_2$ shows a higher limited oxygen index (LOI) at 50 and 55% loading, but the smaller primary particle size may result in a better grade in UL-94 tests. At the high loading of 60%, all samples with any preparation methods exhibit V-0 grade but the LOI value depends on not only primary particle size but also dispersion state.