On the verse, "And Aharon was one hundred and twenty-three years old," the Jerusalem Talmud states: "The one hundred and twenty-three times that Israel responds 'Halleluyah' correspond to the years of Aharon." This requires explanation: what is the connection between the recitation of Hallel and the years of Aharon?
This can be understood by first noting that the Rambam brings this practice in the laws of Chanukah. He describes the original manner of reciting Hallel in the days of the early Sages, when all the people would answer "Halleluyah" after every verse, and concludes, "This was the original custom, and it is the proper way to conduct oneself."
Although this practice was originally instituted because many people in those days were not proficient in reciting Hallel themselves, the Rambam indicates that this manner of recitation possesses an intrinsic advantage. It creates unity in the recitation of Hallel, for everyone participates in a single, shared proclamation of praise.
Ordinarily, under the principle of "one who hears is considered as though he has responded," there remains a distinction between the one reciting the Hallel and those listening. However, when everyone answers "Halleluyah," it is regarded as though they all recited the very same Hallel together, creating a unified act of praise.
This explains its connection to Aharon, whose defining quality was that he "loved peace and pursued peace." The Torah itself emphasizes this in connection with the count of Aharon's years, where it states, "The entire House of Israel wept for Aharon," because he devoted himself to bringing peace between people.
It may also explain why the Rambam places the laws of Hallel in the Laws of Chanukah rather than in the Laws of Prayer. The concluding theme of the Laws of Chanukah is peace, ending with the statement that "the entire Torah was given to bring peace into the world." The communal recitation of Hallel, which unites all Jews in a single expression of praise, is therefore especially appropriate in this context.