Venn diagrams have got to infiltrate the modern curricula as a way to explain probability theory, discussing sets of events. Not surprising, and we can say that they never left us really in topology and other usages of the lattice of union and intersection of sets.
Now, I have recently noticed that they are being used also for a different task, the analysis of factors of integer numbers and polynomials, and the subsequent calculation of the greatest common divisor and least common multiple.
In fact there are two different usages here: simply to represent the set of divisors of two numbers A and B and its intersection, $A \cap B$ or directly represent the aggregates (?) of prime factors of A, B and its gcd, $A \wedge B$. The first way is very in the spirit of New Math, but in order to be able to expose the LCM it needs, I believe, to use $AB=LCM \times GCD$.
The second way is more explicit, one gets the LCM, as $A \vee B$, by multiplying all the factors in the diagram and the GCD by restricting to only the "wedge" part of it.
But we can not see the factors as elements of a set, because of course we can have repeated factors. The problem appears when we remember that the number of subsets of a set is $2^N$, but the number of divisors of 12 = [2,2,3] needs of course to account for the repetition.
Still it looks, this second way, an useful representation and I am tempted to use it. The caveats are:
Could it cause to the student some contradiction with other usages of the diagrams, as e.g. in probability theory?
Is it actually a good tool to understand the concept? I mean, compared with the usual recipe of writing both numbers as a prime factorization and choosing the upper / lower exponent.