The offer that is given to the twelve is understood as a personal reward. This contrasts to the previous question asked of the Savior at what appears to have been the beginning of this visit with the twelve:
3 Nephi 27:2
2 And Jesus again showed himself unto them, for they were praying unto the Father in his name; and Jesus came and stood in the midst of them, and said unto them: What will ye that I shall give unto you?
We do not know how it is that “What will ye that I shall give unto you?” was a question that elicited a discourse on the name of the church, but “What is it that ye desire of me” should elicit a personal request. Clearly this was the intent of the Lord, that they should receive some desired blessing for their service.
All but three of the twelve desire to come speedily to the kingdom of God after their work on earth is done. This is a righteous desire, for they believe in the promise of the kingdom and were willing to do their work before they received their reward.
That the Savior should mark their time on the earth as “seventy and two years” is curious. The number appears this way in counts of the tribes carried into Babylonian captivity, but only for two of the tribes (see Ezra 7:3-4; Nehemiah 7:8-9), but this does not appear to have any particular meaning that influences the number we see in this text. It is possible that the number is an extrapolation of three days (72 hours) into a figure of a “perfect” time related to the number 3 as a representation of the Godhead. This would be a number that would be significant to a Christian community after understanding the Father, Son and Holy Ghost, which was apparently part of the information communicated or understood as part of the visits of the Savior to the New World. Three would not have been a Mesoamerican number. For a Mesoamerican culture outside of the Christian influence, we would have expected a number that was either built on base 20, or in multiples of 4. This number would be significant in the Christian context, however, based upon the three members of the Godhead.