Commentary on the Bible, by Adam Clarke, [1831], at sacred-texts.com
David divides the families of Eleazar and Ithamar, by lot, into twenty-four courses, vv. 1-19. How the rest of the sons of Levi were disposed of, Ch1 24:20-31.
Nadab and Abihu died before their father - That is, during his lifetime.
Eleazar and Ithamar executed the priest's office - These two served the office during the life of their father Aaron; after his death Eleazar succeeded in the high priesthood. And under Eli the high priest, the family of Ithamar re-entered into that office.
And Ahimelech - Ahimelech is put here for Abiathar, who was high priest in the days of David. Abiathar had also the name of Ahimelech, as well as his father. See Calmet.
They divided by lot - This prevented jealousies: for, as all the families were equally noble, they had equal right to all ecclesiastical and civil distinctions.
And Shemaiah - "Moses the great scribe, who is called Shemaiah, the son of Nethaneel, of the tribe of Levi, wrote them down." - T.
One principal household - for Eleazar - The family of Eleazar was the most illustrious of the sacerdotal families, because Eleazar was the first-born of Aaron, Ithamar's family was the second in order and dignity; therefore one of the principal families of Eleazar was first taken, and then one of Ithamar's, and thus alternately till the whole was finished.
Under Aaron their father - That is, they followed the order and plans laid down by Aaron during his lifetime.
The sons of Merari - It is remarkable that not a word is here spoken of the family of Gershom.
These likewise cast lots - The Levites were divided into twenty-four orders; and these were appointed by lot to serve under the twenty-four orders of the priests: the first order of Levities under the first order of priests, and so on. The meaning is not very clear: "both elder and younger," says Bishop Patrick, "had their places by lot, not by seniority of houses. They who were of greater dignity drew lots against those who were of less; and were to take their courses according to the lot they drew." This may have been the case; but we are very little interested in the subject.