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Until what day of the month may Kiddush Levana be said?
Kiddush Levana may only be recited within the first half of the month. A lunar month consists of 29 days, 12 hours and 793 Chalakim. Thus, it may only be said up to 14 days 18 hours and 396.5 chalakim [i.e. 22 minutes] past the Molad. [However, there are opinions who allow it to be said until 15 complete days past the Molad. Other opinions allow in a time of need to say Kiddush Levana with a blessing up until the night of the 16th of the month, including the night of the 16th. Others rule it may even initially be said in a time of need up until 15 days 12 hours and 22 minutes from the Molad, which is 18 hours past the time of the first opinion. Others suggest it may be said even past this time [up until the end of the month]. Others allow saying it past this time [up until the end of the month] if one says it from the Tur or Gemara. Practically, initially one is to be very careful to recite Kiddush Levana prior to the end time of the first/earliest opinion.]
Coming up in Part 2: How we rule Bedieved if first time passed; How to calculate the end time according to any opinion
One is to beware to recite Kiddush Levana prior to 14 days 18 hours and 396.5 chalakim past the Molad. If it is past this time-See Part 2!
 Rama 426:3; Bach; Shlah; Chayeh Adam 118:14; Kitzur SHU”A 97:10; Kaf Hachaim 426:53
Ruling of Michaber: Kiddush Levana may be said up to 15 days past the Molad. Once the 16th day past the Molad has begun it may no longer be said. [ibid] These days are calculated as 24 hour days and not by weekdays. [M”A 426:12; M”B 426:17] Thus according to the Michaber one has 6 more hours to say Kiddush Levana past the time of the Rama.
Ruling of Kaf Hachaim for Sefardim: The Kaf Hachaim 426:53 concludes that one is to follow the opinion of the Rama in these matters, as Safek Brachos Lehakeil, even against the Michaber.
Ruling of M”B: The M”B rules one may be lenient like Michaber. [Biur Halacha “Velo Tes Zayin Bechlal”]
 There are 1080 Chalakim in an hour. [Tur 427]
 The month begins at the time of the Molad of that month. Hence, one can say Kiddush Levana until the above time passes from the Molad and he is not to calculate it from Rosh Chodesh. [Michaber ibid]
Other Opinions: Some write one counts the above time not from the Molad but from Rosh Chodesh. [Taamei Haminhagim p. 200; See M”A 426:12]
 Michaber ibid; Mor Uketzia, and so concludes Biur Halacha “Velo Tes Zayin Bechlal”
 Kneses Hagedola in name of Rabbeinu Peretz; Heishiv Moshe 14; Tzeror Chesed; Shoel Umeishiv Kama 3:151; brought in Chasam Sofer 102 [brought in Alef Lamagen 581:22]; The Rebbe in 1961 15th Sivan said Kiddush Levana 1.5 hours past the time. The Rebbe stated he relies on the Chasam Sofer ibid; Rabbi Mordechai Perlow states that he remembers that a number of times they said Kiddush Levana in Lubavitch on the night of the 16th from a Gemara Sanhedrin
 Chasam Sofer ibid that it may even initially be said up until 18 hours past the time of the Rama
 The reason: As it takes 18 hours for the effects of the moon to be seen on earth. Thus, the diminishing of the moon is not visible to earth until this time. [Chasam Sofer ibid]
 Suggestion in Chasam Sofer 102; Directive of Rebbe Maharash and Rebbe Rashab in Shemuos Vesipurim p. 184
The Chasam Sofer 102 defends saying Kiddush Levana with a blessing even within the second half of the month if one receives much joy from this, such as when the moon had not been seen the entire month and one looks forward to seeing it as a good omen. [See Teshuvah there for the exact case of allowance of Chasam Sofer] His reasoning is because it is a blessing of praise to Hashem for the joy and benefit of the moonlight. Nevertheless, he does not permit it unequivocally as is understood there from the Teshuvah. From the testimony of Reb Yaakov Landau recorded below it is evident that the Rebbe Maharash and Rebbe Rashab allowed saying Kiddush Levana even past the 16th of the month, and even without using a Gemara. The Rebbe Rashab once said Kiddush Levana 17 days past the molad. It was said with a blessing and not from a Gemara. [Memoirs of Rav Yaakov Landau, brought in Shemuos Vesipurim p. 184 see below]
 Divrei Torah 4:107; Darkei Chaim Veshalom 495; See also Avnei Nezer 383; Taamei Haminhagim p. 199 brings from Derech Pekudecha in name of the Chozeh Melublin that after the time has passed one may nevertheless read the blessing from the Gemara. Alef Lamagen 581:22 concludes from Derech Pekudecha that so is the custom of the world to say it from a Gemara with a blessing after the correct time; Mentioned in words of Rebbe Rashab in Shemuos Vesipurim p. 184; See Sheilas Yaavetz 81 that one may mention Hashem’s name when reading a blessing in the Talmud; Many Poskim however forbid doing so. [See M”A 215:5; Birkeiy Yosef 215 that so is custom of elderly Rabbis; Machazik Bracha in name of Tashbatz Katan 419 in name of Maharam, brought in Shaareiy Teshuvah 215:4; P”M 215 A”A 5; M”B 215:14]
 Gemara Sanhedrin 42a
 Kaf Hachaim 426:53 that so applies even for Sephardim that they should suspect for the opinion of Rama ibid