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When reciting Hallel responsively (the chazzan saying each stich of Hallel, and the congregation responding "Halleluyah"), they say "Halleluyah" 123 times. The Yerushalmi (Shabbos 16:1) associates this with the age of Aharon, and this is codified by Rambam (Hil. Chanukah 3:12).
In one of his talks (Likkutei Sichos, vol. 23, pp. 229ff), the Lubavitcher Rebbe zt"l explains the deeper reason behind this association: (a) this way of saying Hallel helps even those who aren't so literate be able to join in the recitation; (b) it means that everyone is reciting Hallel in unison. Both of these reflect Aharon's way of bringing everyone, regardless of their status, closer to Hashem ("אוהב את הבריות ומקרבן לתורה").
W.M. Feldman, in his book Rabbinical Mathematics and Astronomy (1931, reprinted 1978), suggests a cycle in which 123 out of every 334 years are leap years (instead of the 19-year cycle with 7 leap years that we use today), so that it keeps better pace with the solar year.
(This is of course of theoretical interest only, since we don't have a Sanhedrin that can make any such changes - and when we do, we'll go back to having Rosh Chodesh and leap years set on an observational basis, so that there won't be any fixed cycles.)