Bristol Crown Court heard one victim, aged 16, was assaulted by five Somali men after she was moved to the city while in the care of another authority.
Her 14-year-old sister was raped by a member of the gang while visiting her.
The inquiry led to police uncovering another gang of Somali origin who had been abusing four other girls.
The four teenagers were paid £30 or given drugs, alcohol and gifts to perform sex acts on older men from the Somali community.
The court heard some were persuaded to have sex with other gang members as they were told by the gang it was Somali "culture and tradition" and "men always have sex with each other's girlfriends".
One 13-year-old victim was raped four times by three different men in a Premier Inn in Bristol city centre.
A statement from the Bristol Somali community said: "The community is deeply shocked and shaken by the outcome of this case. They are unforgivable acts of cruelty against the most vulnerable members of our community."
The 13 men, all from Bristol, were convicted of charges including rape, sexual activity with a child, facilitating child prostitution, trafficking and paying for the sexual services of a child.
Six were jailed following a trial during the summer. The remaining seven were convicted on Wednesday.
Details of the two cases - which found grooming and abuse dating back to 2011 - can only now be revealed after reporting restrictions were lifted.
The first trial centred on a group of drug dealers from the Easton area and their exploitation of primarily one teenage girl.
She had been moved into a flat on her own in the city and left almost unsupervised by social workers from outside the area.
The second trial focused on another group of young men and their grooming and subsequent sexual abuse of girls.
Tried in July and sentenced for up to 13 years in jail:
Mustapha Farah, 21, Liban Abdi, 22, and Arafat Osman, 20, were each jailed for 13 years for paying for the sexual services of a child and supplying Class A drugs
Abdulahi Aden, 20, was jailed for 13 years for rape and supplying Class A drugs
Mustafa Deria, 22, was found guilty of rape and was jailed for seven-and-a-half years
Idleh Osman, 22, was jailed for 10 years for facilitating child prostitution and supplying Class A drugs
Tried in November and due to be sentenced on Friday:
Sakariah Sheik, 21, Abdirashid Abdulahi, 21, and Jusuf Abdirizak, 20, were found guilty of rape
Mohamed Dahir, 22, was found guilty of causing child prostitution
Omar Jumale, 20, was found guilty of having sex with a child
Said Zakaria, 22 was found guilty of rape and having sex with a child
Mohamed Jumale, 24, was found guilty of sex with a child
Crying under a sink
Speaking in July, Judge Michael Roach said the gang took "considerable advantage" of the 16-year-old girl who had been moved to Bristol by a council, which cannot be named in order to protect her identity.
"I hope there will be an opportunity for the authorities to reconsider their thinking behind such a placement because it has, on any retrospective view, added considerably to the damage of that young person," he said.
The teenager had been ordered by a court to live outside her home area and was placed in "supported living accommodation".
Social workers had "very real concerns" about her and tried to persuade her to leave but "she refused to", the court heard.
The abused girl's five-month ordeal ended when police went to her flat looking for her sister who had been reported missing.
The 14-year-old sibling was found crying in a cupboard under the kitchen sink in just her underwear.
"One of the women police officers went to speak to her and she said that one of the men had forced himself on her, he had raped her," prosecutor Anna Vigars said in court.
An independent serious case review into her care is now being carried out.