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Elvis Aaron Presley was an American singer, actor, and musician. A cultural icon, he is commonly known simply as Elvis and is also sometimes referred to as "The King of Rock 'n' Roll" or "The King".
Presley began his career in 1953 as one of the first performers of rockabilly. Presley had a versatile voice and had unusually wide success encompassing many genres, including rock and roll, gospel, blues, country, ballads and pop.
To date, he is the only entertainer that has been inducted into four music halls of fame.
In the 1960s, Presley made the majority of his 31 movies, most of which were poorly reviewed but financially successful musicals. In 1968, he returned to live performances in a television special, and performed across the U.S., notably in Las Vegas.
In 1973, Presley staged the first global live concert via satellite (Aloha from Hawaii), reaching at least one billion viewers live and an additional 500 million on delay.
Presley was an untrained musician who played guitar and piano entirely by ear. In response to that, Elvis said,
I don't read music, but I know what I like."
In 1956, Presley began his acting career in film. He screen-tested for Paramount Pictures by lip-synching "Blue Suede Shoes" and performing a scene as 'Bill Starbuck' in The Rainmaker. Despite being confident that The Rainmaker would be his first film role, the part went to Burt Lancaster.
After signing a seven-year contract with Paramount, Presley made his big-screen début with the musical western, Love Me Tender. It was panned by the critics but did well at the box office.
The majority of Presley's films were musical comedies made to "sell records and produce high revenues. He also appeared in more dramatic films, like Jailhouse Rock and King Creole.
Presley movies were sometimes poorly received but none the less very popular, and he "became a film genre of his own.
For those too young to have experienced Elvis Presley in his prime, today’s celebration of the 25th anniversary of his death must seem peculiar. All the talentless impersonators and appalling black velvet paintings on display can make him seem little more than a perverse and distant memory. But before Elvis was camp, he was its opposite: a genuine cultural force... Elvis’s breakthroughs are underappreciated because in this rock-and-roll age, his hard-rocking music and sultry style have triumphed so completely."
– The New York Times
As far as it's known, the two Kings - of Rock 'n' Roll and of Pop - never performed together. Elvis died 13 days before Michael Jackson turned 19.

Lisa Marie, the common "human connection" between Elvis & Michael Jackson (Photo/wiki)
Michael married Elvis' only daughter Lisa Marie in 1994, but Michael first met her in 1975 when Elvis was still alive. What we do know that the Kings had in common was their love for music and family. And the one mutual bond that they ended up having was Lisa Marie Presley.
Obviously they must have been aware of each other as talents. But no source, the writer knows of, indicates if the two Kings ever met, let alone perform together. The following video may get as close to them being together as was possible. ~ If anyone knows any of the above, if the two Kings met or performed together, please indicate so in a comment.