The least basic metal hydroxide among the following is-

1.  $\mathrm{Mg}{\left(\mathrm{OH}\right)}_{2}$

2.  $\mathrm{Ca}{\left(\mathrm{OH}\right)}_{2}$

3.  $\mathrm{Sr}{\left(\mathrm{OH}\right)}_{2}$

4.  $\mathrm{Ba}{\left(\mathrm{OH}\right)}_{2}$

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. $\mathrm{Be}{\left(\mathrm{OH}\right)}_{2}$ and $\mathrm{Mg}{\left(\mathrm{OH}\right)}_{2}$ 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.

The magnitude of hydration energy remains almost same whereas lattice energy decreases down the group leading to more negative values for $∆{\mathrm{H}}_{\mathrm{solution}}$ down the group.

More negative $∆{\mathrm{H}}_{\mathrm{solution}}$ more is solubility of compounds.
Hence, $\mathrm{Be}{\left(\mathrm{OH}\right)}_{2}$ and $\mathrm{Mg}{\left(\mathrm{OH}\right)}_{2}$ have less negative values for $∆{\mathrm{H}}_{\mathrm{solution}}$ hence, least basic.