Sidnicka Wilson was arrested near Western Avenue and Martin Luther King Boulevard at about 3:30 p.m. after a citizen flagged down police officers.
The citizen pointed officers to a vehicle where Wilson was found with a man, according to the LAPD.
Wilson initially gave police a false name. Officers verified her identity using a photograph and distinguishing marks on her body. She eventually admitted her real name.
She was booked at the LAPD 77th Station.
Wilson was booked on charges of child abuse and possession of rock cocaine and drug paraphernalia. She was held on $100,000 bond.
Wilson said she left the children with her boyfriend on Sunday, according to the LAPD.
The kids, ages 2 and 3, were found near Manchester and Stanford avenues around 9 a.m. Monday. A Good Samaritan noticed the younger child heading toward traffic and stopped him. Another person spotted the 3-year-old wandering into a nearby apartment building, followed him and called police.
Authorities determined that the boys lived with Wilson in an apartment building on the 600 block of E. 85th Street. Investigators are unsure if the boys were left in the care of someone else or abandoned the children. Police are also trying to determine if something has happened to her.
"Inside the apartment, it was in deplorable conditions, not fit for a child," said LAPD Capt. Lillian Carranza.
Carranza said in an earlier incident, the 3-year-old was found in a nearby liquor store getting a loaf of bread to feed himself and his little brother.
The boys were placed under custody of the Los Angeles County Department of Children and Family Services.
Anyone with information regarding this crime is asked to contact LAPD 77th Division, Detective Tavares or Jones at (213) 485-4175. During non-business hours or on weekends, calls should be directed to (877) LAPD-24-7. Anyone wishing to remain anonymous should call Crime Stoppers at (800) 222-TIPS. Tipsters may also contact Crime Stoppers by texting to phone number 274637 (C-R-I-M-E-S on most keypads) with a cellphone. All text messages should begin with the letters "LAPD." Tipsters may also go to LAPDOnline.org, click on "web tips" and follow the prompts.