Since no one is justified before God by the law, we know that Jesus could not have fulfilled the Mosaic Law by perfect obedience to it. Therefore, Jesus must have fulfilled the Law of Moses through love, as prescribed by Romans 13:8 "for he who loves his fellow man has fulfilled the law." This is consistent with what Jesus himself told his disciples "greater love has no one than this, that he lay down his life for his friends." This is exactly what Jesus did for us. By this greatest act of love he fulfilled the Law of Moses. By this same act he fulfilled the law of Christ, since he bore our sinful burdens on the cross.
What many do not understand is that the Law of Moses is fulfilled when its purpose is fulfilled not when it is obeyed perfectly. Once the Law of Moses has been fulfilled it can be set aside because it has served its purpose for those who have put their faith in Jesus Christ.
What is the purpose of the Law of Moses if perfect obedience is not required for its fulfillment? The Law of Moses was given to show how sinful we are. The law was put in charge of us, as a slave-master, to lead us to Christ so that we might be justified by faith. But those to whom faith has come are no longer under the supervision of the law. So for them the Law of Moses is set aside because God's purpose for the Law of Moses has been fulfilled in their life when they believe in Jesus Christ. Christ is the end of the law so that there may be righteousness for everyone who believes.
Although it is true that those to whom faith has come are no longer under the supervision of the law since Christ is the end of the law for everyone who believes. This is not true for those who do not believe in Jesus as their Lord and savior. Scripture tells us that the law is good if one uses it properly and is not made for the righteous but for lawbreakers. If this is the case should we encourage those who do not believe in Jesus to live by the Law of Moses? No! We should encourage everyone to believe in Jesus so they can be saved from their sins and be reconciled to God. This is something the Law of Moses can't do.
Having said this, there is a very good use for the Law of Moses yet; for believers and non-believers alike. It should be used to instruct everyone in matters relating to God. By studying it we can better know and understand the character of God, how he does things, and what is important to him. Because all Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, so that the man of God may be thoroughly equipped for every good work. This includes the Law of Moses.
The Law of Moses is very similar to the rules used with small children. There are a great deal of "do this" and "don't do that" type of rules. As children grow these early rules become a part of their character rather than the focus of their attention. As children grow they will instinctively obey the fundamental rules of their youth without having to focus on them. When they become of age they can focus on other things like living their life and accomplishing goals.
Just as these childhood rules remain with us for life, so to the Law of Moses will always affect the way believers live their lives because it shows us the character of the God we love. Once we have learned all that the Law can teach us of God we are prepared to have a meaningful relationship with him by loving him. When we love him we no longer have to look to the Law of Moses for direction but we can look to God Himself in the person of the Holy Spirit that lives in us when we believe. Now all communication with God and direction from God is personal because we love him and he loves us. The Law of Moses prepares us for a relationship with God, following the Holy Spirit is the relationship with God. The Law of Moses was only intended as a means to an end, our relationship with God is the end. That is why Scripture says that Christ is the end of the law. Once we have a relationship with Jesus, the purpose of the Law of Moses has been fulfilled and is forever relegated to reference material for the believer.