Thanks to fordivfactored and forfactored and all the arithmetic functions accepting [n, factor(n)] it's common to work with the factorization matrix. Is there a convenient way to multiply two factored numbers?
Of course you can hack this together. If n and m are relatively prime, then their factored forms fn = factor(n) and fm = factor(m) can be found with
fmn = concat(fm~, fn~)~
but this is not sorted. So
fmn = vecsort(concat(fm~, fn~), 1)~
and teasing out the common factors should be just a bit more work.
Obviously factor(vecprod(apply(factorback, [fm, fn]))) would work but it defeats the whole purpose of having the numbers factored in the first place.