George VI passed in early 1952, and Elizabeth was coronated was June 2, 1953. She has reigned during 12 different American Presidents' tenures. Elizabeth was queen while Truman was President, but they did not meet while in those capacities. She never met with Lyndon Johnson.
Thus, Queen Elizabeth II has met with 10 sitting US Presidents.
Elizabeth met President Truman in 1951 while a princess and filling in for her ailing father. In fact, she carried a draft accession declaration with her on her North American trip in case her father died while she was out of the United Kingdom.
Queen Elizabeth met former President Herbert Hoover in 1957.
Elizabeth did not travel with her father and mother (Queen Elizabeth) when they met with President Roosevelt in June 1939. The visit was historic; it was the first visit by a British monarch to North America in history.
Queen Victoria is the only British monarch to have reigned during more American Presidents' tenures. She became Queen shortly after Martin Van Buren (the 8th) took office, on June 20, 1837, and died on January 22, 1901, shortly before Theodore Roosevelt (the 26th) left office. Although she never met any of the men, she reigned over a span of 19 Presidents.