Long before it became shorthand for cannabis culture, 420 was already a mathematically tidy number: it's the least common multiple of every integer from 1 through 7 — the smallest value that 1, 2, 3, 4, 5, 6, and 7 all divide into evenly. That makes it a genuinely useful number for splitting things into halves, thirds, quarters, fifths, sixths, or sevenths without a remainder, a property with real practical value in scheduling and measurement long before it acquired its more famous modern association.
That modern association traces to a specific, well-documented origin rather than a vague folk legend. In the fall of 1971, a group of five students at San Rafael High School in California — who called themselves "the Waldos" because they hung out by a particular wall — agreed to meet at 4:20pm, after sports practice, at a statue of Louis Pasteur on campus to search for a reportedly abandoned cannabis crop supposedly planted by a Coast Guard service member who could no longer tend it. They never found the crop, but "420" (or "420 Louis") stuck as their private code for cannabis use, shorthand that outlasted the treasure hunt that inspired it.
The phrase spread through Bay Area counterculture with an assist from the Grateful Dead scene — several of the Waldos had family and social connections to the band's circle — and later High Times magazine helped carry it to a national and eventually international audience through the 1990s. April 20th (4/20) became an informal annual date associated with cannabis culture and, later, cannabis-legalization activism, while 4:20pm developed a parallel reputation as an informal "time" for the same association.
A persistent but false urban legend claims 420 was California police radio code or penal code for marijuana-related offenses. It wasn't — California's actual cannabis-related statute at the time was Penal Code 647(f) and later Section 11357, unrelated numbers entirely. The myth likely spread precisely because it offered a tidier, more "official-sounding" origin story than the real one, but the Waldos' own account, corroborated by later journalism and their own preserved memorabilia from the era, is the well-documented version historians and journalists who've investigated the claim generally accept.
Mathematically, 420 factors as 2² × 3 × 5 × 7 — the product of the first four primes, with an extra factor of 2 — which is exactly what makes it divisible by every integer from 1 to 7 in the first place: its prime factorization contains enough copies of 2, along with single copies of 3, 5, and 7, to cover every number in that range. This isn't a coincidence tied to the number's later fame; it's a direct, checkable consequence of how LCM calculations work, and 420 would have this property regardless of any cultural association layered onto it decades later.
420 also shows up as a genuinely common number outside both contexts — it's a frequent unit in recipe scaling, event planning, and any situation needing a total divisible cleanly across a wide range of small group sizes, which is the same mathematical property (its rich set of divisors: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420 itself) doing quiet, unglamorous practical work in contexts that have nothing to do with its cultural reputation.
Twenty-four divisors is a genuinely large count for a three-digit number, though it's worth being precise that 420 doesn't quite qualify as what number theorists call a "highly composite number" — a formally defined category (numbers with more divisors than every smaller positive integer) that includes nearby values like 360 and 840 but skips 420 itself, since 360 already reaches twenty-four divisors at a smaller size. 420 is nonetheless unusually divisor-rich for its size, sitting close to that formally exceptional company without technically qualifying — a useful, honest distinction between "genuinely has a lot of factors" and the specific, stricter mathematical definition of "highly composite." Even is 420, obviously, and its digit sum (4+2+0=6) confirms its divisibility by both 2 and 3 at a glance, well before any full factorization is needed.
The Waldos themselves reportedly kept ephemera from the era — letters, a flag, and other memorabilia referencing "4:20" — which later surfaced and were examined by journalists investigating competing origin claims, lending the group's account a level of physical documentation that most competing folk explanations for the term's origin simply lack. That documentation is a large part of why the Waldos' story, rather than any of the several rival explanations that circulated over the decades, is the version treated as authoritative by outlets that have specifically investigated the term's history.