A book called "Hamlet's Mill," by Giorgio de Santillana and Hertha von Dechend (who are both professors of the history of science at MIT and Johann Wolfgang Goethe-Universität, respectively) covers this material well. By examining similarities in mythology and religion across many cultures and times, many of them shown to be thematically related to the story which eventually became Hamlet, they promulgate the idea that ancient, prehistoric human culture wasn't simply inarticulate superstitious people making up tales by the campfire. Their central thesis was that there was an educated class of people in prehistoric times who encoded their teachings, specifically astronomic, in the language of what we read as story and myth. Possibly because of retelling by people who don't understand what they're saying, much of this comes to modern ears as story and folktale. The number 72 is specific as it has to do with both the precession of the equinoxes and the amount of time that the star Sirius is out of view in the night sky every year. Therefore that number, and some of its factors, show up in many myths.

It's an extremely dense book and can be hard to read at over 300 pages and another 39 appendices which go into extreme depth about many of the sources that the authors used in writing, as well as an exhaustive index.

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In the Abrahamic tradition, this comes down to something called gematria. Basically, because the Hebrew language used the same characters for both letters and numbers, any word may be given a numerical value. By extension, there exists a branch of Jewish mysticism (kabbalah) that entails looking at verses, or even whole chapters, as giant equations. Words that have the same gematria values are thought to have a sort of mystic connection.

It's hard to explain much further, because it takes years of study to even grasp the basics, but I can sort of show you why 72 is an interesting number from this perspective. If you break it down to its prime factors you get 2^3 × 3^2. Look at the symmetry there, keeping in mind that 2 and 3 have great symbolic value in almost every world culture, 2 representing union or duality, and 3 usually symbolizing completeness. 2^3 = 8, and it just so happens that 8 is the small gematria (every word actually has several values) of "Torah" (the books of Moses ), "good" (tov), and at least two different names for God, including the tetragrammaton ("Yahweh"). 72=8×9, and 9 is 3 times itself, so thrice complete. The ancient Hebrews didn't fail to notice that if you multiply any number by nine and then add the digits, you get 9 again; this is one of the core principles of gematria. 9 is also, it must be noted, the small gematria of Adam's name (so in a certain way, 72 = God x Man), and the first time that the digit appears in the Bible, it's the first letter of "good," as in, "God looked on his creation, and it was good."

So this may all seem like total bullshit, but many ancient peoples took numbers very seriously. I can't speak to Chinese or Muslim numerology, but if you look at the numerical properties of 72, it's easy to see why totally unrelated cultures might attach great significance to it.

EDIT: just noticed the mod post. Hope this doesn't break the math rule.

In the Judaic and Christian traditions, the symbolic importance of the number 72 occurs over a very long period. It is easy now to look back and point out all the instances of the number in the traditions (72 original nations, 72 languages, 72 translators of the Septuagint, 72 elders at Sinai, 72 disciples of Christ, etc), but it is really the momentum that begins to build that makes the number important in, at least, certain Christianities. But the origins of this numerical symbolism are vague.

For instance, Genesis 10, which is often put forth as a starting point for the tradition in Judaism and Christianity and to some degree Islam, is a list of names of Noah's descendants. Excluding his three sons, people have counted either 71 descendants (in the Hebrew) or 73 (in the Septuagint). But because 70 seems to have some symbolic importance for Jewish thinkers (maybe because of the early importance placed on 7 and 10), the number 71 was rounded down. (This also likely explains some of the variants you see: 70 elders at Sinai, 70 translators of the Septuagint, 70 disciples of Christ).

But the number 72 was also symbolically important for Jewish and Christian thinkers (probably because of the symbolic importance of 6 in ancient Greek math, the first perfect number, and 12 in Jewish thought: 6 x 12 = 72). This combo is used in the Letter of Aristeas to come to the total of 72 translators.

This combination of numerical symbolism mixed with desire to align with past authorities begins to build the tradition. Late antique Christian writers, especially, start bringing in new uses of the number, which really takes off when it is used in Luke 10 (which in turn may be alluding to Genesis 10, or perhaps the number of translators). Later authors typically connect the number to earlier uses: for example, 72 hours Christ spent in the tomb (Bede); 72 bishops needed to condemn another bishop (standard medieval canon law), 72 books of the Bible (Isidore), etc.

So ignoring those hazy origins (likely in a cultural symbolic importance of the duodecimal system, but who knows), it is clear that later instances simply build on earlier uses of the numerical symbol somewhat arbitrarily.

Many other numerical connections can be made across religious traditions that seem to be completely coincidental, and this may be one of those cases.

For more info, Arno Borst, Turmbau von Babel is the main authority on the number, if you can read German. I can probably dig out some old article titles (also likely in German), if there is interest.

Strictly from a Chinese perspective, 72 naturally arises from adding the 64 hexagrams to their 8 constituent trigrams.

Off the top of my head, I can't think of tales of 8 particularly special disciples of Confucius (unlike the 8 Taoist Masters or the 8 Immortals), but I'd imagine that that would be the numerological split: one master, eight special teachers, 64 disciples.

That's how the I Ching is structured.

If you're unfamiliar with the bagua, or 8 trigrams, they're what you get when you take the Tao (1), split it into yin and yang (2), then split those into sets of three yin or yang elements - so you might get yin-yin-yin (kun, earth), or yin-yang-yin (kan, water), or... 8 possible combinations, all representing a kind of fundamental building block of the world.

Start combining trigrams into hexagrams, and you have 64 possible combinations.

This is pretty fundamental to East Asian culture - eight is a lucky number, a polite number of gifts, and the bagua show up everywhere from martial arts (bagua zhang was what the "good" Jet Li used in The One) to the South Korean flag.