Ruth was the great-grandmother of which famous king?

Answer: David

Ruth's son Obed became the father of Jesse, and Jesse was the father of David.

“The neighbor women said, “A son has been born to Naomi,” and they named him Obed. He became the father of Jesse, the father of David. Salmon was the father of Boaz, Boaz was the father of Obed, Obed was the father of Jesse, and Jesse was the father of David.”— Ruth 4:17, 4:21-22 (BSB)