Kiwoom does not have a postseason-clinch number; they can miss the postseason even if they win all 56 of their remaining games.
Here is scenario in which Kiwoom wins 56 additional games (82 total) but does not reach the postseason.

Here are the final standings in the scenario:
            Team	W	L	D	PCT	GB
              LG	86	56	2	0.6056	0.0
             KIA	83	58	3	0.5887	2.5
           Lotte	83	58	3	0.5887	2.5
             SSG	83	58	3	0.5887	2.5
         Samsung	83	59	2	0.5845	3.0
          Kiwoom	82	59	3	0.5816	3.5
          Doosan	56	85	3	0.3972	29.5
              KT	56	85	3	0.3972	29.5
          Hanwha	52	90	2	0.3662	34.0
              NC	41	97	6	0.2971	43.0

To construct the scenario, we start with the current standings:
            Team	W	L	D	GL	PCT	GB
          Hanwha	49	33	2	60	0.598	0.0
              LG	46	37	2	59	0.554	3.5
           Lotte	46	37	3	58	0.554	3.5
             KIA	45	37	3	59	0.549	4.0
             SSG	42	39	3	60	0.519	6.5
              KT	43	40	3	58	0.518	6.5
         Samsung	43	41	1	59	0.512	7.0
              NC	37	40	5	62	0.481	9.5
          Doosan	34	48	3	59	0.415	15.0
          Kiwoom	26	59	3	56	0.306	24.5

The next two tables show, respectively, how many of their remaining games each team wins and ties against each of the other teams in the scenario:

					Scenario Additional Wins Against
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Wins
Doosan	-	7	0	0	4	0	0	7	0	4	22
Hanwha	0	-	0	0	3	0	0	0	0	0	3
KIA	7	8	-	0	4	4	0	9	0	6	38
Kiwoom	6	6	4	-	4	7	7	7	8	7	56
KT	0	5	0	0	-	0	0	8	0	0	13
LG	8	6	4	0	9	-	8	5	0	0	40
Lotte	7	6	7	0	4	0	-	8	5	0	37
NC	0	4	0	0	0	0	0	-	0	0	4
Samsung	4	8	6	0	9	4	1	6	-	2	40
SSG	5	7	0	0	8	4	5	7	5	-	41
-----------------------------------------------------------------------------------
Losses	37	57	21	0	45	19	21	57	18	19

					Scenario Additional Draws (Ties) With
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Total
Doosan	-	0	0	0	1	0	0	2	0	0	0
Hanwha	0	-	0	0	0	1	0	1	0	0	0
KIA	0	0	-	2	0	0	0	0	0	1	0
Kiwoom	0	0	0	-	0	0	0	1	0	0	0
KT	0	0	0	0	-	0	2	0	0	0	0
LG	0	0	0	0	0	-	1	0	0	0	0
Lotte	0	0	0	0	0	0	-	0	0	0	0
NC	0	0	0	0	0	0	0	-	1	1	1
Samsung	0	0	0	0	0	0	0	1	-	1	1
SSG	0	0	0	0	0	0	0	0	0	-	0
-----------------------------------------------------------------------------------
Total	0	0	0	0	0	0	0	1	1	0

The next two tables show, respectively, how many total games each team wins and ties against each of the other teams in the scenario:

					Scenario Total Wins Against
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Wins
Doosan	-	11	2	7	8	4	4	9	5	6	56
Hanwha	5	-	5	9	8	4	4	7	5	5	52
KIA	14	11	-	6	11	8	6	13	3	11	83
Kiwoom	9	7	8	-	7	10	9	9	11	12	82
KT	7	8	5	9	-	4	4	11	5	3	56
LG	12	11	8	6	12	-	12	11	6	8	86
Lotte	12	12	10	7	10	3	-	12	12	5	83
NC	5	8	3	6	5	5	4	-	3	2	41
Samsung	11	11	13	5	11	10	4	12	-	6	83
SSG	10	11	4	4	13	8	11	13	9	-	83
-----------------------------------------------------------------------------------
Losses	85	90	58	59	85	56	58	97	59	58

					Scenario Total Draws (Ties) With
Team	Doosan	Hanwha	KIA	Kiwoom	KT	LG	Lotte	NC	Samsung	SSG	Total
Doosan	-	0	0	0	1	0	0	2	0	0	3
Hanwha	0	-	0	0	0	1	0	1	0	0	2
KIA	0	0	-	2	0	0	0	0	0	1	3
Kiwoom	0	0	0	-	0	0	0	1	0	0	3
KT	0	0	0	0	-	0	2	0	0	0	3
LG	0	0	0	0	0	-	1	0	0	0	2
Lotte	0	0	0	0	0	0	-	0	0	0	3
NC	0	0	0	0	0	0	0	-	1	1	6
Samsung	0	0	0	0	0	0	0	1	-	1	2
SSG	0	0	0	0	0	0	0	0	0	-	3
-----------------------------------------------------------------------------------
Total	3	2	3	3	3	2	3	6	2	3