The Greek translation of the Hebrew scriptures is called the Septuagint, from the Latin for seventy, and abbreviated LXX. The name comes from a legend that will not sit still at seventy.
The Letter of Aristeas, a Jewish work in Greek usually dated to the second century BCE, tells how Ptolemy II Philadelphus, wanting the Jewish law for the library at Alexandria, wrote to the high priest in Jerusalem, who sent seventy-two elders, six from each of the twelve tribes, with a scroll. The seventy-two worked on the island of Pharos and completed the translation in seventy-two days. Later retellings, in Philo and then in Christian writers, embellish the story considerably, adding that the translators worked in separate cells and produced identical texts, which the Letter itself does not claim.
So the tradition gives seventy-two and the name gives seventy. The rounding is ancient and nobody has satisfactorily explained it; the likeliest account is simply that seventy was already the conventional number for such a body, and the more awkward seventy-two was smoothed to it.
The same wobble occurs in the New Testament. At Luke 10:1 Jesus appoints and sends out either seventy or seventy-two disciples, and the manuscript evidence is genuinely divided, with strong early witnesses on each side. Modern critical editions and translations differ, and the choice is often read against the seventy or seventy-five nations of Genesis 10, since the mission is being presented as a mission to the world.
Historically, the Letter of Aristeas is not a reliable account of how the translation happened. What it records is how Alexandrian Jews wished to present a translation that had already become authoritative.