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The last common ancestor refers to the most recent possible shared ancestor between two individuals, species, or groups of life. For instance, the last common ancestor of all animals is thought to have existed about 610 million years ago, though it may be much older. We can infer some of its features by looking at commonalities held by all living animals. For instance, the fundamentals of cellular metabolism are held in common among all animals.
There are two ways to figure out the last common ancestor of two subjects, and they're both imperfect. The first is to dig up fossils and make guesses about their place in the evolutionary tree, based on morphology and other clues. This can fail because interpretations can be incorrect, and the vast majority of all species never left any fossils. The second is to look at the genomes of living animals and see how much information they have in common. The less shared genetic information, the more distantly related to two are, and the differences between genomes can be used to estimate the approximate time of divergence. This approach can also fail, because species evolve at different rates that we can't always predict.
The last common ancestor of all life — sometimes called last universal common ancestor, or LUCA — lived between 3.6 and 4.2 billion years ago, an extremely long time ago, even by the standards of paleontologists. The common ancestor of animals lived at least 610 million years ago, as mentioned earlier. That of all vertebrates was probably a jawless fish that lived 530 million years ago, in the Early Cambrian. The last common ancestor of all terrestrial vertebrates was a lobe-finned fish that started crawling on land 375 million years ago. These fish are the direct ancestors of all human beings.
The last common ancestor of all living mammals existed at least 125 million years ago. The last common ancestor of all primates existed between 55 and 85 million years ago, while the last one of hominids ("great apes": humans, chimpanzees, orangutans, and gorillas) lived about 18 million years ago. Orangutans, gorillas, and chimps split from other primates 14, 8, and about 7 million years ago, respectively. Until recently it was thought that the ancestors of humans split from chimps 3-5 million years ago, but new fossils discoveries have suggested that this divergence took place earlier than initially thought.
The last common ancestor of all living humans lived only about 3,000 years ago, making us all very closely related. There is some confusion with the identification of "Mitochondrial Eve," believed to be the matrilineal most recent common ancestor (MRCA) of all living humans, who lived about 170,000 years ago. The matrilineal MRCA can only be traced through female DNA, however, and cannot be directly linked as a common ancestor of all humans.