LOS ANGELES — A man who authorities believe strangled dozens of women as he moved from place to place around the country was convicted Tuesday of three 1980s murders in Los Angeles.Samuel Little, 74, appeared almost cheerful as he was found guilty of crimes that will send him to prison for life without chance of parole.He chatted with his lawyer during the 10-minute hearing. Asked by Superior Court Judge George G. Lomeli whether he agreed with a Sept. 25 sentencing date, Little replied causally, "It's your discretion.""Well, I need an answer," the judge said."Sure — you're welcome," Little responded.Defense attorney Michael Pentz did not speak to reporters after the hearing.Jurors deliberated just two hours before convicting him of three counts of first-degree murder.The women were found nude below the waist and had been dragged into debris-strewn alleys.Prosecutors linked the former boxer to the killings through evidence found at the scenes, which they compared to his DNA profile in a criminal database.In 2012, Los Angeles detectives found Little living in a shelter in Kentucky and arrested him.Little's victims were 41-year-old Carol Alford, whose body was found on July 13, 1987; 35-year-old Audrey Nelson, found on Aug. 14, 1989; and 46-year-old Guadalupe Apodaca, found on Sept. 3, 1989.Apodaca's son, Tony Zanbrano, 50, said his own life had been blighted by his mother's death and a quarter-century of not knowing who had killed her."I was totally happy, grateful that this nightmare is ended, knowing that he won't be on the streets to hurt somebody else," he said outside court. "He was a monster. He'd thrive on killing mothers.""My life has totally changed now ... everything is turning out for the best," he added.Apodaca's niece, Diana Flores, 56, said she was glad "that nobody else will feel the pain and the grief that he caused so many children out there."During trial, prosecutor Beth Silverman said Little is likely responsible for at least 40 killings since 1980. Authorities in California, Florida, Kentucky, Missouri, Louisiana, Texas, Georgia, Mississippi and Ohio are looking for possible links."It's the end of an entire career of killing," she said after the verdict.It was difficult to track down Little and required help from law enforcement agencies from all over the country, Los Angeles police robbery-homicide Detective Mitzi Roberts said."He wouldn't stay in one place more than a week or two and then he would move on to the next one," she said.Little's victims were easy targets because they were drug-users and prostitutes on the fringes of society, authorities said."These perpetrators are cowards that prey on the weak and the vulnerable in the darkest hours of the night where there won't be anybody to see them," Roberts said.Little already had been arrested in connection with crimes in 24 states, mostly assault, burglary, armed robbery, shoplifting and drug violations. Over 56 years, Little served less than 10 years in prison, authorities said.