Least basic compound among the following would be

\(Lu(OH)_3\)

The correct answer is option 2. \(Lu(OH)_3\).

Lanthanum (La), Cerium (Ce), Gadolinium (Gd), and Lutetium (Lu) are all elements in the Lanthanide series. As we move across this series from left to right, the size of the lanthanide ion (Ln³⁺) steadily decreases due to a phenomenon called lanthanide contraction. This contraction affects the basicity of the corresponding hydroxides \((Ln(OH)_3)\).

Reasoning:

Lanthanide Contraction: As the size of the \(Ln^{3+}\) ion decreases, the force of attraction between the positively charged ion and the negatively charged hydroxide ions \((OH^-)\) increases. This stronger electrostatic attraction makes it harder for the hydroxide to donate a proton (H⁺) in water, reducing its basic character.

\(Lu(OH)_3\) has the smallest \(Ln^{3+}\) ion among the given options: Therefore, \(Lu(OH)_3\) will have the strongest attraction between the lanthanide ion and hydroxide ions, making it the least basic compound when compared to \(La(OH)_3\), \(Ce(OH)_3\), and \(Gd(OH)_3\).

Therefore, Lutetium hydroxide \((Lu(OH)_3)\) is the least basic compound due to the lanthanide contraction effect.