This is what I have so far. Nothing I can make much sense of, but maybe will help everyone else.
The nth term in sequence K is: (49 - n)/[2|3] where '[2|3]' means 'either 2 or 3', but I haven't yet figured out when to use 2 instead of 3 or vice versa.
Similarly, the nth term in sequence H is: n*[1|2|3|4]
Rewriting the sequences with the variable choices yeids:
I'm guessing that we need to figure out the rules behind the 2 sequences and extend them out far enough to find the corresponding pairs that K and H quote at the very end (112,21), (93,9), (48,0.5), (84,14), (18,10.3), (84,7) and that the values of n for each entry will end up corresponding to a 6 letter word.
Since the H sequence involved [1|2|3|4], I decided to try that as well for the K sequence. I'm still not sure how to decide which multiplier/divisor is used, so I opened a spreadsheet and calculated all 4 possible H and K sequence numbers for n=1:48. I then looked for n's where both the final values quoted by H and K were existing for that value of n. That yielded the following sequence 28,31,48,21,18, 28.
I still don't know if this sequence is significant nor how to convert it to a word.