James,
These three Gospels - Mark, Matthew, and then Luke - were written by different people at different times for different readerships for very different purposes.
No NT writer, including these, either saw or heard Jesus. They relied on the traditions that were passed on in their respective communities.
So it should not be any surprise that they disagreed with one another.
The initial Christians were not documenters (probably not literate). They fully expected the Coming and God's Kingdom to take place shortly, so why write? Even Jesus - who shared their expectations - did not write anything.
The earliest NT record comes from Paul, and he does not describe Jesus' life or his words. He too expected Jesus to "come" during his lifetime, and his letters address short-term local issues based on the final days of Jesus' life.
The Gospels started to emerge after Paul's death, after the destruction of Jerusalem. "Luke" was not even a Jew, His Gospel is as unreliable as his book of Acts.
An interesting direction of research would be to study scholarly works that seek to determine which of the words ascribed to Jesus were likely genuinely uttered by him. I have seen estimates that 25% can be considered as genuine.
Doug