When they say "most repeated occurrances" of a factor, I don't think they mean "in each factorization", but "in any one". For instance, 4 and 8 each contain factors of 2, but 8 contains three copies, so that's what you use: three copies of 2. The factorizations of 12 and 18 each contain factors of 2 and 3; 12 contains two copies of 2 and one of 3, while 18 contains one of 2 and two of 3. You use two copies of each, for an LCM of 2*2*3*3 = 36.
In your case, the one factorization is 3*3*7 and the other is 3*19. You need one 7 (because that's the most that any of the factorizations contains), one 19 (for the same reason), and two 3s. While the one factorization contains only one 3, the other contains two 3s, and you need to include whatever is the maximum number of copies from either of the factorizations.
For further information, try here.