Question

Why are lanthanum and actinium at the bottom of the periodic table?

Answer 1

The periodic table is organized in a way in which trends with certain things such as ionization energy or atomic radius would "work out". It also have increasing atomic mass.

It's also organized to tell you the electron and proton of each element, least to greatest. (the atomic number) Example: Chlorine has 17 protons and 17 e-
(Left to right)
(Top to bottom)

Lanthanum and actinium play the role of being in the bottom because of their large atomic radius and having many protons/electrons.
They're also in the F block for electron configuration.