The surname langmuir was first found in East Dunbartonshire at Langmuir, near Kirkintilloch, a town and former royal burgh about 8 miles (13km) northeast of Glasgow. Alternatively the name could have been derived from Longmore, near Ayr.  One of the first records of the name was Elice de la Longmore and Robert de Langemore of Ayrshire who rendered homage to King Edward I in his invasion of Scotland in 1296. 
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Migration of the langmuir family
Some of the first settlers of this family name or some of its variants were: John Langmore settled in Plymouth in 1620; Anne Longmore settled in Virginia in 1739; John Longmore arrived in Philadelphia in 1876.