According to Angela Crowell and John Tvedtnes, in Judaism [and contrary to the custom of Joseph Smith's time], while a brief blessing is recited before eating, a series of longer blessings, the birkat ha-mazon, follows the meal. . . . The basis for this practice is Deuteronomy 8:10, which calls for a blessing only if one has eaten and is full:
When thou hast eaten and art full, then thou shalt bless the Lord thy God for the good land which he hath given thee.
Blessing the Lord after eating one's fill ensured that the Israelites would not forget the source of their blessings (Compare Deuteronomy 6:11-12; 31:20; Nehemiah 9:25-26).
It is interesting to compare this practice with the wording of Alma 8:22, "And it came to pass that Alma ate bread and was filled; and he blessed Amulek and his house, and he gave thanks unto God." Here, too, the blessing and thanks to God are offered only after being "filled." . . .
John W. Welch has noted that an early Christian document, Didache 10:1-2,5, enjoins prayer "after being filled" during communion. In this connection, it is interesting to see that similar thoughts are expressed on both occasions when the resurrected Christ blessed the sacrament for the Nephites. In 3 Nephi 18:8-18 we read that the Nephites partook of the bread and wine and "were filled" (3 Nephi 18:9), after which Jesus instructed them to pray. Third Nephi 20:9 contains the slight variation that "when the multitude had all eaten and drunk, behold, they were filled with the Spirit; and they did cry out with one voice, and gave glory to Jesus, whom they both saw and heard." In this case, the people were filled not with the bread and wine, but with the Spirit. Nevertheless, it is interesting that they "gave glory to Jesus" on this occasion. [Angela M. Crowell and John A. Tvedtnes, "The Nephite and Jewish Practice of Blessing God after Eating One's Fill," in Journal of Book of Mormon Studies, 6/2 1997, pp. 251-254] [See the commentary on 3 Nephi 20:9]