Where in Scotland did Macbeth meet his death in 1057?

According to the play by William Shakespeare [Baptized April 26, 1564-April 23, 1616], Macbeth died on the battlefield outside Dunsinane Castle. According to historical records, Macbeth [d. August 15, 1057] may have died, or been mortally wounded, in the battle at Lumphanan. If mortally wounded, he may have died a few days later in Scone. Either way, he was buried in the royal burial grounds on the island of Iona, off the western coast of Scotland. Ironically, that also was the final resting place of his predecessor, King Duncan I [d. August 14, 1040]. Neither did the play agree with the historic records as to who killed Macbeth. According to the play, it was Macduff. According to the historic record, it was King Duncan's son, the future King Malcolm III [d. November 13, 1093].