KOORI - How does the burnt offering in the OT relate to Jesus and his life? Why must it be fully consumed, and how do we see this fulfilled in Jesus life?

JOEL - Adam was told that the sacrifices he made was in similitude of the atoning sacrifice of Christ (Moses 5:7).
In the Mosiac system (Lev. 9: 2-3, 7, 10, 12-14, 16-17, 22, 24) Christ can represent the sacrificial offering, the priest performing the ordinince, and the one offering the sacrifice.
The sacrifice had to be a male animal without blemish (goat, bullock, dove, etc); a representation of Jesus who lived an entire life without sin.
The Levitical priest acted as the mediator standing between God and man; another representation of Christ who is the great mediator between us and God(2 Ne. 2: 27-28, 1 Tim. 2: 5). This has not changed in present day, for it is the priest in the Aaronic or Levitical Priesthood who kneels at the sacrament table to bless both bread and water(D&C 20:46).
In the instance of the burnt offering Christ can also be seen as the offerer, in the sense that He must comply with all ritual "to fulfill all righteousness", as He did when he was baptized by John (Matt 3:15). Those offering the sacrifice would lay their hands on the sacrificial animal, symbolizing transference of their sins of the people to the animal (Num. 8:10-12).
Among the offerings called for in the Mosaic law, only the burnt offering was to be entirely consumed. This was a representation of the complete submission of Jesus to the will of God for the salvation of His children. A similar promise is also made by present day saints who covenant to live the law of sacrifice; to give all our heart, might, mind, and strength to the building of the kingdom of God (D&C 4:2).