D&C 20

We learn that it is after we follow the gospel or doctrine of Christ exhibiting faith in Jesus Christ in that  -

"...we know that all men must repent and believe on the name of Jesus Christ, and worship the Father in his name, and endure in faith on his name to the end, or they cannot be saved in the kingdom of God."  (Doctrine and Covenants  Section 20:29)

And having been baptized and received the Gift of the Holy Ghost (Section 20) that -

"...we know that justification through the grace of our Lord and Savior Jesus Christ is just and true;
31 And we know also, that sanctification through the grace of our Lord and Savior Jesus Christ is just and true, to all those who love and serve God with all their mights, minds, and strength."  (Doctrine and Covenants  Section 20:30 - 31)

The consequence of faith, repentance, baptism for the remission of sins, receiving the Gift of the Holy Ghost, and enduring to the end brings about justification and sanctfication through the atonement of Jesus Christ.

In my mind, justification is satisfying the demands of justice or in other words, becoming more like the Savior.  The Savior's atonement fulfils the demands of justice, if we satisfy the conditions He has outlined.  Thus justice is satisfied and mercy is extended.  Justification then requires two players...the repentant and obedient and another that satisfies the demands of justice or punishment.

Sanctification is the process of overcoming the natural man and becoming clean and worthy to serve.  An actual cleansing, purification, and refining process.  Such process again has conditions dependent on faithfulness "to all those who love and serve God with all their mights, minds, and strength."  Thus -

"...by the water ye keep the commandment; by the Spirit ye are justified, and by the blood ye are sanctified..."  (Pearl of Great Price Moses 6:60)

I sense that as we partake of the sacrament, our mind and heart turns to remembrance of His body and blood suggesting the price of His body paid for justification and the price of His blood to be cleansed.   I personally do not understand how the blood actually sanctifies and cleans us, but in faith, I believe that it provides the power to the Holy Ghost to do so.  Paul taught this doctrine to the Corinthians -

"Know ye not that the unrighteous shall not inherit the kingdom of God? Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor abusers of themselves with mankind,
10 Nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God.
11 And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God."  (New Testament  1 Corinthians 6:9 - 11)