Answer by taking a quote from the following article:

Charles-Edouard Jeanneret, known as Le Corbusier (French: [l@ koRby'zje]; 6 October 1887 - 27 August 1965), was a Swiss-French architect, designer, painter, urban planner, writer, and one of the pioneers of what is now called modern architecture. He was born in Switzerland and became a French citizen in 1930. His career spanned five decades and he designed buildings in Europe, Japan, India, and North and South America.

Le Corbusier moved to Paris definitively in 1917 and began his own architectural practice with his cousin, Pierre Jeanneret (1896-1967), a partnership that would last until the 1950s, with an interruption in the World War II years  In 1918, Le Corbusier met the Cubist painter Amedee Ozenfant, in whom he recognised a kindred spirit. Ozenfant encouraged him to paint, and the two began a period of collaboration. Rejecting Cubism as irrational and "romantic", the pair jointly published their manifesto, Apres le cubisme and established a new artistic movement, Purism. Ozenfant and Le Corbusier began writing for a new journal, L'Esprit Nouveau, and promoted with energy and imagination his ideas of architecture.  In the first issue of the journal, in 1920, Charles-Edouard Jeanneret adopted Le Corbusier (an altered form of his maternal grandfather's name, Lecorbesier) as a pseudonym, reflecting his belief that anyone could reinvent themselves. Adopting a single name to identify oneself was in vogue by artists in many fields during that era, especially in Paris.  Between 1918 and 1922, Le Corbusier did not build anything, concentrating his efforts on Purist theory and painting. In 1922, he and his cousin Pierre Jeanneret opened a studio in Paris at 35 rue de Sevres. His theoretical studies soon advanced into several different single-family house models. Among these was the Maison "Citrohan", a pun on the name of the French Citroen automaker, for the modern industrial methods and materials Le Corbusier advocated using for the house. Here, Le Corbusier proposed a three-floor structure, with a double-height living room, bedrooms on the second floor, and a kitchen on the third floor. The roof would be occupied by a sun terrace. On the exterior Le Corbusier installed a stairway to provide second-floor access from ground level. Here, as in other projects from this period, he also designed the facades to include large uninterrupted banks of windows. The house used a rectangular plan, with exterior walls that were not filled by windows but left as white, stuccoed spaces. Le Corbusier and Jeanneret left the interior aesthetically spare, with any movable furniture made of tubular metal frames. Light fixtures usually comprised single, bare bulbs. Interior walls also were left white.

Did he exhibit with famous members of the Cubist movement?
Ozenfant encouraged him to paint, and the two began a period of collaboration. Rejecting Cubism