An MS-13 sign painted on rocks in a nature area in the vicinity of Veirs Mill and Randolph roads in Silver Spring, Md. (Michael Williamson/The Washington Post)

A federal judge on Tuesday sentenced three local leaders of a violent Salvadoran gang to lengthy prison terms for a ­2 1/2 -year run of killings, stabbings and beatings across the Washington area.

A D.C. federal jury convicted Noe Machado-Erazo, a.k.a. Gallo, 32, of Wheaton, Md.; Jose Martinez-Amaya, a.k.a. Crimen, 28, of Brentwood, Md.; and Yester Ayala, a.k.a. Freeway or Daddy Yankee, 24, of the District in August 2013 of conspiracy to commit racketeering and murder ­charges as members of La Mara Salvatrucha, or MS-13.

Twelve other defendants charged in 2010 previously pleaded guilty.

Senior U.S. District Court Judge Royce C. Lamberth of the District sentenced Machado-Erazo and Martinez-Amaya to life plus 10 years in prison and Ayala to 30 years in prison.

Prosecutors alleged that MS-13 “cliques,” with such names as the Sailors, Normandy, Peajes, Uniones and Fultons, collaborated across the District, Maryland and Virginia, controlled by ringleaders or “big homies” imprisoned in El Salvador or at large in Central America or Mexico.

Working through a partnership they call La Hermandad, or the Brotherhood, clique capos known as shot callers — or La Palabra — approved the killing of rivals, beating of informants, extortion and drug dealing in competition with other local Latino gangs.

Victims of the defendants, a jury found, included 14-year-old Giovanni Sanchez, who was stabbed to death and left in a street in Columbia Heights in Northwest Washington in December 2008; former gang member Louis Alberto Membreno-Zelaya, whose stabbed body was found in Northwest Washington in November 2008; and Felipe Leonardo Enriquez, 25, who was fatally shot and dumped on sewage utility property near the Montgomery and Howard county line in March 2011.

“This prosecution shows our commitment to purging MS-13’s bloody brand of violence from the District of Columbia,” acting U.S. attorney Vincent H. Cohen Jr. said in a statement with U.S. Assistant Attorney General Leslie R. Caldwell of the criminal division, D.C. Police Chief Cathy L. Lanier and Special Agent in Charge Clark E. Settles of the U.S. Immigration and Customs Enforcement’s Homeland Security Investigations’ D.C. field office.

“These killers brought lawless vengeance to our community and left a 14-year-old boy dead. These gang members will now have decades in prison to reflect on their heinous crimes,” Cohen said.