What famous family ruled Florence during Michelangelo's life?

Florence in the 15th century was ruled by the famous Medici
family, the most famous member of which was probably Lorenzo de' Medici.  This family was not
only powerful and influential over life in Florence, but they had close ties to French Kings, the
rulers of other Italian city states, and most people of power who were in the know during their
reign knew to deal directly with the head of the Medici family rather than the other parts of the
Florence government.

Lorenzo, also known as Lorenzo the Magnificent,
was very important in the creative and productive history of Michelangelo because he was a very
generous and consistent patron of the arts, and Michelangelo's first patron.  He commissioned
paintings, frescoes and sculptures, and left a lasting impression on the art and cultural history
of Florence.