The "truly wicked, marauding mob" stabbed Sean McHugh, 19,  with a "sword stick" in Anfield on 30 September 2013.
Reese O'Shaughnessy, 19, was jailed for a minimum of 18 years after he was convicted alongside four others.
Andrew Hewitt, 15, Keyfer Dykstra, Corey Hewitt and Joseph McGill, all 14, were also detained by Liverpool Crown Court.
Dykstra was sentenced to a minimum of 12 years, Andrew Hewitt and McGill were sentenced to a minimum of nine years and Corey Hewitt for a minimum of six years.
Judge Clement Goldstone described Mr McHugh's killers as "a marauding mob".
"Each of you has been convicted of the murder of Sean McHugh - a truly wicked attack in which each of you played different roles," Justice Goldstone said.
A victim impact statement from Mr McHugh's mother Lorraine that was read in court said: "They might as well have killed me."
The teenagers were part of a gang known as the Lane Heads, a rival gang to the Walton Village Heads which Mr McHugh was linked to.
Months earlier, Dykstra was stabbed in the chest by a member of the Walton Village Heads and wanted to "avenge that stabbing", the court heard.
"The stabbing was avenged not by attacking the person responsible, but by attacking someone... by virtue of his affiliation to the Walton Village Heads," Justice Goldstone said.
The gang targeted Mr McHugh, of Beckett Street, Liverpool, after a minor dispute and found him at the Priory Road launderette, where he had left his washing, at about 19:00 BST.
Armed with knives and the makeshift sword stick, described as similar to a broom handle but with a blade attached, the gang forced the back door to the room where Mr McHugh was hiding.
He was beaten and stabbed before the group ran out.
Mr McHugh escaped and was found in an alleyway having been stabbed in the groin. He died a few days later in hospital from blood loss.
Five teenagers who murdered a man in a Liverpool launderette when some of them were 13 years old have been sentenced.