Verses

In two places in the New Testament the genealogy of Jesus son of Mary is mentioned: Matthew 1:6-16 and Luke 3:23-31

Each gives the ancestors of Joseph the CLAIMED husband of Mary and Step father of Jesus.

The first one starts from Abraham(verse 2) all the way down to Jesus.

The second one from Jesus all the way back to Adam. The only common name to these two lists between David and Jesus is JOSEPH.

How can this be true?