From lanthanum to lutetium, the lanthanide or lanthanoid family of chemical elements consists of 15 metallic chemical elements with atomic numbers 57?71. The rare-earth elements, which include these plus the chemically related elements scandium and yttrium, are commonly referred to as rare-earth metals. Lanthanides are a group of 15 chemical elements whose atomic numbers range from 57 to 71. In the 5d shell, each of these elements has one valence electron. The elements have qualities in common with the group's initial member, lanthanum. Lanthanides are silver-colored metals that are reactive. Lanthanide atoms are most stable in the +3 oxidation state, but the +2 and +4 oxidation states are also frequent. Although lanthanides are commonly referred to as "rare earth," they are not exceptionally uncommon elements. They are, nevertheless, difficult to distinguish from one another.
Lanthanides have a wide range of scientific and industrial applications. Catalysts for the manufacture of petroleum and synthetic goods are made from their components. Lamps, lasers, magnets, phosphors, motion picture projectors, and X-ray enhancing screens all employ lanthanides. Precipitation with an appropriate reagent separates rare earth elements from other elements in a mineral. Because their chemical characteristics are similar, it's difficult to separate rare earth elements using conventional chemical methods, and isolating a single element can take hundreds of fractional crystallizations. The isolation of a single rare earth element can be achieved with more simplicity and precision using ion-exchange technologies.

It is Lutetium, because with gaining more mass the the electrons more closer to the core and  it undergoes so called into lanthanoid contraction.