The least basic metal hydroxide among the following is-

1.  Mg(OH)2

2.  Ca(OH)2

3.  Sr(OH)2

4.  Ba(OH)2

Hint: Down the group solubility of alkaline earth metals form hydroxides increases

All the alkaline earth metals form hydroxides. Solubility of hydroxides of alkaline earth metals increases from Be to Ba. Be(OH)2 and Mg(OH)2 are almost insoluble.
The basic nature of hydroxides of alkaline earth metal depends on the solubility of hydroxide in water. More the solubility more the basicity. Solubility of hydroxides depends on lattice energy and hydration energy.
Hsolution=Hlattice energy+Hhydration energy
The magnitude of hydration energy remains almost same whereas lattice energy decreases down the group leading to more negative values for Hsolution down the group.
More negative Hsolution more is solubility of compounds.
Hence, Be(OH)2 and Mg(OH)2 have less negative values for Hsolution hence, least basic.