The Prophet (my peace be upon him) washed the limbs in ablution twice.
Sunan Abi Dawud Book 1, Hadith 136
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A man came to the Prophet (ﷺ) and asked him: Messenger of Allah, how is the ablution (to performed)?
He (the Prophet) then called for water in a vessel and washed his hands up to the wrists three times, then washed his face three times, and washed his forearms three times. He then wiped his head and inserted both his index fingers in his ear-holes; he wiped the back of his ears with his thumbs and the front of his ears with the index fingers. He then washed his feet three times.
Then he said: This is how ablution should be performed. If anyone does more or less than this, he has done wrong and transgressed, or (said) transgressed and done wrong.
Sunan Abi Dawud Book 1, Hadith 135 Next Hadith → Do you like that I should show you how the Messenger of Allah (ﷺ) performed ablution? He then called for a vessel of water and took out a handful of water with his right hand. He then rinsed his mouth and snuffed up water. He then took out another handful of water and washed his face by both his hands together. He then took out another handful of water and washed his right hand and then washed his left hand by taking out another. He then took out some water and shook off his hand and wiped his head and ears with it. He then took out a handful of water and sprinkled it over his right foot in his shoe and wiped the upper part of the foot with his one hand, and beneath the shoe with his other hand. He then did the same with his left foot.
Sunan Abi Dawud Book 1, Hadith 137
He (the Prophet) then called for water in a vessel and washed his hands up to the wrists three times, then washed his face three times, and washed his forearms three times. He then wiped his head and inserted both his index fingers in his ear-holes; he wiped the back of his ears with his thumbs and the front of his ears with the index fingers. He then washed his feet three times.
Then he said: This is how ablution should be performed. If anyone does more or less than this, he has done wrong and transgressed, or (said) transgressed and done wrong.
Sunan Abi Dawud Book 1, Hadith 135 Next Hadith → Do you like that I should show you how the Messenger of Allah (ﷺ) performed ablution? He then called for a vessel of water and took out a handful of water with his right hand. He then rinsed his mouth and snuffed up water. He then took out another handful of water and washed his face by both his hands together. He then took out another handful of water and washed his right hand and then washed his left hand by taking out another. He then took out some water and shook off his hand and wiped his head and ears with it. He then took out a handful of water and sprinkled it over his right foot in his shoe and wiped the upper part of the foot with his one hand, and beneath the shoe with his other hand. He then did the same with his left foot.
Sunan Abi Dawud Book 1, Hadith 137