The Story of Lot in Sodom & Gomorrha

Why did The Lord destroy these cities? And How did he save Lot and his family?

Jude1:7
“Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire.

Genesis 18-20 Then the LORD said, “The outcry against Sodom and Gomorrah is so great and their sin so grievous 21that I will go down and see if what they have done is as bad as the outcry that has reached me.
If not, I will know.

32 Then he said, “May the Lord not be angry, but let me speak just once more. What if only ten can be found there?” He answered, “For the sake of ten, I will not destroy it.”