In the following table, I highlight differences between the two lineages given for the Savior.  Underlined individuals might be the same person in each line.

Matt. 1:2 – 17

Luke 3:23 – 38 (modified to be in reverse order for comparison with Matt.)

17 So all the generations from Abraham to David are fourteen generations; and from David until the carrying away into Babylon are fourteen generations; and from the carrying away into Babylon unto Christ are fourteen generations.   1.     Abraham (all the same in this section) 2.     Isaac 3.     Jacob 4.     Judas 5.     Phares 6.     Esrom 7.     Aram 8.     Aminadab 9.     Naasson 10.  Salmon 11.  Booz 12.  Obed 13.  Jesse 14.  David   1.     David 2.     Solomon 3.     Roboam 4.     Abia 5.     Asa 6.     Josaphat 7.     Joram 8.     Ozias 9.     Joatham 10.  Achaz 11.  Ezekias 12.  Manasses 13.  Amon   14.  Josias (same as 15?)       Into Babylon 1.     Josias 2.     Jechonias 3.     Salathiel  (same as 22) 4.     Zorobabel  (same as 23) 5.     Abiud 6.     Eliakim 7.     Azor 8.     Sadoc 9.     Achim 10.  Eliud 11.  Eleazar                   12.  Matthan (the same as 40?) 13.  Jacob 14.  Joseph (same as 42) Jesus (same as ®)

1.     God 2.     Adam 3.     Seth 4.     Enos 5.     Cainan 6.     Maleleel 7.     Jared 8.     Enoch 9.     Mathusala 10.  Lamech 11.  Noe 12.  Sem 13.  Arphaxad 14.  Cainan 15.  Sala 16.  Heber 17.  Phalec 18.  Ragau 19.  Saruch 20.  Nachor 21.  Thara   1.     Abraham 2.     Isaac 3.     Jacob 4.     Juda 5.     Phares 6.     Esrom 7.     Aram 8.     Aminadab 9.     Naasson 10.  Salmon 11.  Booz 12.  Obed 13.  Jesse 14.  David   1.     David 2.     Nathan 3.     Mattatha 4.     Menan 5.     Melea 6.     Eliakim 7.     Jonan 8.     Joseph 9.     Juda 10.  Simeon 11.  Levi 12.  Matthat 13.  Jorim 14.  Eliezer 15.  Jose 16.  Er 17.  Elmodam 18.  Cosam 19.  Addi 20.  Melchi 21.  Neri 22.  Salathiel 23.  Zorobabel 24.  Rhesa 25.  Joanna 26.  Juda 27.  Joseph 28.  Semei 29.  Mattathias 30.  Maath 31.  Nagge 32.  Esli 33.  Naum 34.  Amos 35.  Mattathias 36.  Joseph 37.  Janna 38.  Melchi 39.  Levi 40.  Matthat 41.  Heli 42.  Joseph Jesus

Legal Successors vs Literal Lineage

One possible explanation is that Matthew’s account is of the lineage of the Savior traced through the rightful heirs of the kingdom, or birthright, and Luke is the literal linage.  James E. Talmage, Jesus the Christ, Ch.7, p.85 – p.86 states:

…. The consensus of judgment on the part of investigators is that Matthew’s account is that of the royal lineage, establishing the order of sequence among the legal successors to the throne of David, while the account given by Luke is a personal pedigree, demonstrating descent from David without adherence to the line of legal succession to the throne through primogeniture or nearness of kin.

Would this appear reasonable based upon my analysis that Luke has many more people covering the same period (41 verse 27 people)?  Six of these people were before the Babylonian exile, and about 9 after (you might want to check my math here).

So, do young deaths explain what happened?  Not really, because someone still had to have issue, so they must have lived to at least get married.  No, there has to be places where the rightful heir or birthright skipped a generation.  That could happen when a father out lives a son, and the kingship passes directly to his grandson.

But that doesn’t completely explain it either.  Because we would just see additional people inserted in one line, and not show up in the other.  But very few people are the same in both lines.  The rules for determining the kingship and birthright were not simply based upon birth order.  They were more complicated than that.  For example, what happens when there is no male heir?  In that case perhaps it passed to the first male of a brother, or even a cousin.  This could account for large number of difference between the lines.

Mary vs. Joseph

Luke’s record is regarded by many, however, as the pedigree of Mary, while Matthew’s is accepted as that of Joseph…. A personal genealogy of Joseph was essentially that of Mary also, for they were cousins. Joseph is named as son of Jacob by Matthew, and as son of Heli by Luke; but Jacob and Heli were brothers, and it appears that one of the two was the father of Joseph and the other the father of Mary and therefore father-in-law to Joseph.

Rightful Heir

James E. Talmage, Jesus the Christ, Ch.7, p.87

In all the persecutions waged by His implacable haters, in all the false accusations brought against Him, in the specific charges of sacrilege and blasphemy based on His acknowledgment of the Messiahship as His own, no mention is found of even an insinuation that He could not be the Christ through any ineligibility based on lineage. …

At the time of the Savior’s birth, Israel was ruled by alien monarchs. The rights of the royal Davidic family were unrecognized; and the ruler of the Jews was an appointee of Rome. Had Judah been a free and independent nation, ruled by her rightful sovereign, Joseph the carpenter would have been her crowned king; and his lawful successor to the throne would have been Jesus of Nazareth, the King of the Jews.

Consider Yourself

Consider for a moment what is being communicated here.  The LDS Bible Dictionary Chronology of the Bible Chart suggests there was about 1,000 years between David and the Savior.

Do you have any idea who even one of your ancestors was 1,000 years ago, in about 1,000 AD?  There are very few people in the world who do.  It is remarkable that record keeping was done such that his lineage could be given so specifically.

But Why Two?

A 2012 BBC article on this topic presents some interesting facts.

Each generation back, we multiply the number by two. This leads to what is called an exponential increase: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and so on.

It’s not long before we hit huge numbers. Take the specific case of Jesus and King David.

The number of generations between them is at least 35. Luke lists 42 generations down the male line, and Matthew gives an incomplete list of 27.

These numbers agree reasonably well with an average time between generations of 25 or 30 years – an estimate taken from documented historical records from Iceland and Canada.

So back in the time of David, Jesus would have had at least 2 x 2 x 2 x 2 (35 times); in other words 2^35 – or more than 34 billion potential ancestors. That’s far more than the total population of the world, of course.

This is a good illustration of what’s been called the “genealogical paradox”.

What happens in this case is that the number of actual progenitors becomes a much smaller number, and in fact, it is likely that almost everyone in Israel at that time could have claimed King David as an ancestor through one line or another.

In fact about 80% of the people at that time in the past [35 generations back] will be the ancestors of everyone in the present. The remaining 20% are those who have had no children, or whose children have had no children, and so on – in other words, people who were genetic dead-ends.

Apply that to the case of King David. According to this model, he would be a common ancestor of the whole population of the Holy Land somewhere between 20 and 35 generations after his life [it the population of Israel at the time was approximately a million people].

This does not mean that everyone would have had the right to be proclaimed King of Israel.  If strict rules were in place such that only one descendant had the right to be king at any point, and Christ descended from each of those individuals, his heritage would have been unique.  Every individual’s linkage to a progenitor is unique.

What it does show though, is that there were likely a dozen more lines which could have been shown to demonstrate Christ was a descendant of King David.  That’s how genealogy works.