There is no definitive answer to this question as it is impossible to accurately measure the IQ of a person who is deceased. However, there are some estimates that have been made based on the known facts about each Beatle's educational background and their general intelligence.
John Lennon is generally considered to be the smartest of The Beatles, with an estimated IQ of 165. He was the only member of the band who attended university, studying at Liverpool College of Art before dropping out to focus on his music career. He was also known for his quick wit and sharp debating skills, often engaging in verbal sparring with journalists.
Paul McCartney also had a high IQ, estimated at around 155. He did not attend university but he did well in school, achieving 15 O-level passes (the equivalent of today's GCSEs). He was always interested in learning new things and was fascinated by technology, which led him to invent several innovative musical devices used by The Beatles including the bass guitar synthesizer and automatic double-tracking machine.
George Harrison had an IQ estimated at 140. He left school aged 17 without any formal qualifications but he later took evening classes in art and history. He was self-taught on the guitar and became one of the most respected musicians in The Beatles, writing classic songs such as "Here Comes The Sun" and "While My Guitar Gently Weeps".