Phoenix Spencer-Horn’s body was discovered within a flat on Glen Lee at around 12.10pm on Monday.
A 26-year-old man has been arrested in connection and is due to appear at Hamilton Sheriff Court tomorrow.
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Officers remain at the scene however there is no wider risk to the public at this time.
A report has been submitted to the Procurator Fiscal.
Detective Chief Inspector Susie Cairns, Lanarkshire CID, said: “Phoenix’s family are obviously stunned and completely devastated by what has happened and we will continue to support them and those affected during this very distressing time.
“Officers remain at the scene however there is no wider risk to the public.”