As Gordon McCulloch, a local historian from Paisley, Scotland, notes:
"MacBeth was one of Scotland's great Kings, regardless of the erroneous tragedy written by Shakespeare. After taking the Crown and deposing Duncan, he kept peace in the land for almost his entire reign of seventeen years (1040-1057) [I checked the dates in the Encyclopedia Brittanica]. No small feat for the time! However, he married Duncan's widow, Gruoch, possibly to reconcile Duncan's supporters, and took into his house her son 'Lullach', Known as 'Lullach the Fool'.In an additional note, Gordon McCulloch writes:
When Macbeth campaigned in Ireland, his point of departure from Scotland, was the Kirkcubright Coast. He and his forces spent years moving between the two lands on expeditions. It is alleged that Lullach married a local laird's daughter and settled down. Indeed, after Macbeth's death, opponents of Malcolm tried to regain the throne by summoning Lullach (as direct heir) northwards to be their figurehead. They failed and Lullach was killed by Duncan's grandson, Malcolm Canmore, in 1058 at Essie in Strathbogie in the attempted coup.
"Pitullich is another old Scots name, but in no way related to McCulloch or McLullach. Indeed Mac or McCulloch is just the soft spoken border pronounciation of McLullach, the letter 'L' not being pronounced either by Lowlanders, or in the Gaelic."