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Despite Jonathan Quick playing only 20 minutes so far this season, and losing Anze Kopitar, Tyler Toffoli and Marian Gaborik to injuries for extended periods of time, the LA Kings find themselves in a battle for a playoff spot with 31 games remaining.
Here's a breakdown of which teams they have to worry about, and which they don't, in the Western Conference playoff race.

Arizona Coyotes

Colorado Avalanche

These two teams may not be mathematically eliminated from playoff contention, but they may as well be.
If their position in the standings didn't convince you, their recent play against the LA Kings should be sufficient evidence that the Avalanche and Coyotes have a long way to go before reaching contender status.

Chicago Blackhawks

Minnesota Wild

Minnesota's Head Coach Bruce Boudreau has won a Division Title in each of his eight full seasons in the NHL.

The Wild are in first place in the Central Division and show no signs of upsetting Boudreau's streak.
Meanwhile, the Chicago Blackhawks have a comfortable 12-point cushion over the St. Louis Blues (currently fourth in the Central Division).
There's not much to worry about either of these clubs since the top three teams in the Central have no impact on the Kings chances of making the playoffs.

Anaheim Ducks

Edmonton Oilers

San Jose Sharks

It finally happened. It turns out this actually is the Edmonton Oilers' year. The Oilers may not be legitimate Stanley Cup contenders just yet, but Connor McDavid and his supporting cast are a healthy eight points ahead of the Kings and seem destined to make the playoffs for the first time in 10 years.
TEN. YEARS.
These three Pacific Division rivals are all locked within a game or two of each other and it would require an uncharacteristic swoon by one of them for the Kings to break into the top three of the Pacific Division.
Then again … we are talking about the Oilers.
The Oilers, Ducks and Sharks will all factor into whether or not the Kings make the playoffs, but not as much as the teams below.

Dallas Stars

Vancouver Canucks

Winnipeg Jets

With roughly 30 games remaining on the schedule, any of these three teams could at some point go on a run and challenge the Kings for a Wild Card spot.
They're all imperfect teams and their flaws are well documented, and it remains to be seen if any of them decide to be sellers at the NHL trade deadline.
While their proximity to the Kings in the standings means they can't be ignored, barring any late season miracles it doesn't appear highly likely for this trio to factor significantly in the playoff hunt.

Calgary Flames

Nashville Predators

St. Louis Blues

These three teams are realistically battling it out with the Kings for the two Wild Card spots. Either the Predators or Blues will finish third in the Central Division, leaving two spots for the remaining three teams.
The Blues are 4-6-0 in their past 10 games and just fired Head Coach Ken Hitchcock.
Meanwhile, the Predators are on a 7-2-1 run. It would seem the two teams are headed in opposite directions and that the Predators are more likely to be a playoff team. Then again, the Blues have too much recent success to count them out completely.
The Flames are a young team with only one playoff appearance in their previous seven seasons. Trade rumors and coaching criticism have swirled around the Flames from the beginning of the season, but they remain a very dangerous threat.
...a threat which knocked the Kings out of postseason contention in 2014-15.