How is congregational prayer performed if one joins the Imam in the second, third, or fourth rak'ah of Fajr, Dhuhr, Asr, Maghrib, or Isha prayer?

It is prescribed for the latecomer to the prayer to pronounce the opening takbir (Allahu Akbar) and then follow the Imam in his current state. The rak'ah (unit of prayer) whose bowing he did not catch is not counted. What he catches with the Imam is the beginning of his prayer, and he completes what he missed after the Imam says the taslim (salutation of peace).

If he catches the Imam after he has risen from bowing in the last rak'ah, he must make up the entire prayer after the Imam says the taslim. The majority of scholars hold that one catches the congregation by catching the opening takbir before the Imam says the taslim.

Evidence for this includes the hadiths: "When you come to the prayer and we are prostrating, then prostrate, but do not count it as anything. And whoever catches the rak'ah has caught the prayer." Narrated by Abu Dawud. And: "When you come to the prayer, observe tranquility. So, whatever you catch, pray, and whatever you miss, complete." Narrated by Al-Bukhari. And: "When one of you comes to the prayer and the Imam is in a certain state, let him do as the Imam does." Narrated by Al-Tirmidhi.

It is obligatory for the latecomer to intend the obligatory prayer and specify it when pronouncing the opening takbir, then follow the Imam, and then complete the remainder of his prayer after the Imam says the taslim.