You can read the whole series here.
Gethsemane 4. Luke + Mark – Matthew in between. John: off the ledger.
Luke doesn’t have anything on the conversation at Kidron, but he puts it in the supper. Luke has a more upbeat narrative, he doesn’t like to speak badly of the legends of the church (his Gospel is partly shaped by Acts). So he tempers a lot of it. The prophecy about Peter is still there, but in Acts he tells how Peter is fearless in preaching, he’s a heroic figure. This is always true of venerated religious people of the past. We always ignore or minimize their faults and failures. We did the same thing in writing about Joseph Smith in the 1850s. He was practically sinless by some lights. Of course he was nothing like that, but it’s natural and that’s Luke. Remember, he’s writing 50-60 years after the fact. Luke can’t help Judas, there’s nothing really that can be done to mitigate that story. But for the other disciples and Peter in particular, he puts in positive statements about their ultimate fate:
(KJV)
28 Ye are they which have continued with me in my temptations.
29 And I appoint unto you a kingdom, as my Father hath appointed unto me [a kingdom];
30 That ye may eat and drink at my table in my kingdom, and sit on thrones judging the twelve tribes of Israel.
31 And the Lord said, Simon, Simon, behold, Satan hath desired to have you, that he may sift you as wheat: (JST: that he may sift the children of the kingdom as wheat—Peter is portrayed as essential to the flowering of Christianity.)
32 But I have prayed for thee, that thy faith fail not: and when thou art converted, strengthen thy brethren.
Luke’s positive view of Peter is present in Matthew: upon this rock, etc. and in John: feed my sheep. The whole career of the disciples dominates the message rather than in Mark where they run away, and it’s a question as to whether they return at all. There’s no doubt they succeed because Luke has Jesus pray for them. Luke doesn’t beat down the disciples like Mark and to some extent Matthew. The difference represents the way people experience trial and suffering. For many, it can be one of utter horror, rending, tearing the soul. For others it may be great sadness but an anchored one where faithful equilibrium is maintained. The latter is Luke’s view of Jesus (for example, he doesn’t use the terrifying “my God, my God, why have you forsaken me?” Luke has instead, “Forgive them Father, for they know not what they do.” That’s the Lukan way).
John’s account has some of the same elements, but they are in different spots. For example, John’s version of the Last Supper is huge by comparison. He mentions the prediction that the disciples will be offended, but he puts it like this: I’ve said these things to you so that you won’t be offended when the time comes [but you’re going to be scattered](Jn 16:1-4; 16:32). For John (chaps. 1, 5, etc.) Jesus is fully divine all the time. All his acts are voluntary, I lay down my life, take it up again. No one can do anything to me unless I let them. Jesus is consistently Sovereign, always in charge in every scene. At the arrest, he’s in control. He says “I am” and everyone falls to their knees, he makes a bargain with the arresting police: if you want me, then you have to let these others go. Luke is intermediate between John and Mark/Matthew. Jesus is still calm, self-contained, but there isn’t the sense of sovereignty that John has. John has Peter saying he won’t fail (and the denial at the rooster crow), but it’s in chapter 13 at the supper. You get some idea of the complexity of treating the Gospels together.
To sum up, all the Gospels have predictions about the future of the disciples. Judas as betrayer in the last supper, statements about their behavior, positive in Luke, but scandal, scattering, in Mark, Matthew, and John (John puts it in a different spot–remember, John has the supper the day before the one where Mark and the others place it). The Peter prediction is at the supper in Luke and John, at the Kidron in Mark and Matthew. From one point of view, Jesus is concerned about what the Passion will do to (and for) his disciples, it’s very personal. The Evangelists situate the Passion of Jesus in terms of what it means to Christian faith, to the lives of Christians. Christianity is largely a theology of suffering, that all Christians will experience it in different ways with different consequences, but that Jesus comes through it and is yet concerned about their fate, showing the way. We all have to carry a cross.
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By Common Consent, a Mormon Blog 
The distance of the gospels from the events in question really isn’t brought up enough in LDS circles where it often comes across as contemporary accounts. But that distance colors how the authors see things as do the differing situations.
I’m a lifelong active member of the church, and in all the Sacrament Meeting talks, Sunday School and Relief Society classes I’ve experienced, have I ever heard it emphasized that the accounts in the gospels weren’t written as they happened or shortly thereafter. How I wish we had Relief Society lessons on how, when and why the gospels were written, Jewish culture at the time of Christ, the history of Jerusalem, the influence of Greek culture on the church as it was taken to the gentiles, etc. The more I learn of those subjects and others like them, the greater my appreciation for and understanding of scripture. Thank you, WVS, for sharing your insights.