The least basic hydroxide amongst the following would be:

\(Yb(OH)_3\) \((Z = 70)\)

The correct answer is option 4. \(Yb(OH)_3\) \((Z = 70)\).

The basicity of metal hydroxides generally increases as you move down a group in the periodic table. This is because the size of the metal ion increases, leading to weaker bonds between the metal ion and the hydroxide ion, making it easier for the hydroxide ion to dissociate and increase the basicity.

In this case, you're comparing hydroxides of elements from the lanthanide series, which are typically known for their similar properties. However, as you move down the series, the atomic number increases, indicating larger atomic and ionic sizes.

So, among the given options, \(Yb(OH)_3\) (\(Z = 70\)) would likely be the least basic hydroxide because ytterbium (Yb) has the largest atomic number (and hence, the largest ionic size) among the options.

Therefore, the correct answer is: 4. \(Yb(OH)_3\) (\(Z = 70\))