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2. Yom Kippur Katan:
Many are accustomed on Erev Rosh Chodesh Elul to fast and recite the Seder of Yom Kippur Katan, even if they are not particular to do so the rest of the year. However some meticulous men are not accustomed to do so even on Erev Rosh Chodesh Elul, [and so is the Chabad custom].
 Mateh Efraim 581:3; Kaf Hachaim 581:23; See M”A 417:3; Bach 686; M”B 417:4; Kaf Hachaim 417:10 regarding the other months.
 See Shaar Yissachar Elul that the second 40 days which achieved the appeasement of G-d after the sin of the Eigel concluded on the 29th of Menachem Av. It is thus called Yom Kippur Katan as it is similar to the third set of 40 days which concluded on Yom Kippur. It is due to this month that all the other Erev Rosh Chodesh are also called Yom Kippur Katan.
 Otzer Minhagei Chabad 4