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The Rangers completed the no-brainer trade they’d been working on. 

Reilly Smith is headed back to Vegas in exchange for a third-rounder in this year’s NHL draft and center prospect Brendan Brisson, the team announced Thursday afternoon on the eve of the March 7 trade deadline. 

The Rangers will retain 50 percent of the $3.75 million cap hit they had Smith on the books for. 

Flipping the third-round pick they acquired in the Smith deal, the Rangers also acquired left-handed defenseman Carson Soucy from the Canucks. 

Smith was held out of the past three games for roster management purposes. In the final year of his deal at $3.75 million, with an eight-team no-trade list, Smith was one of the most logical trade pieces for management. 

“There’s conversations with Reilly. There are conversations with the team,” Rangers head coach Peter Laviolette said earlier this week. “It’s a different situation, but Reilly was a really good player for us, did a lot of good things, but this is just where it’s at right now.” 

The Rangers acquired Smith from the Penguins in July in exchange for a conditional fifth-round pick in this year’s draft and a second-rounder in 2027. 

After Pittsburgh retained 25 percent of Smith’s $5 million cap hit this past summer, the Rangers were able to retain some of their own this time around to make him an even more attractive trade piece. 

The Rangers were Smith’s third team in the past three seasons, over which he went from winning the Stanley Cup in Vegas to a limited role in Pittsburgh before heading to New York. 

Smith, who spent six of his 14 NHL seasons in Vegas, was part of the inaugural Golden Knights team that went all the way to the Stanley Cup Final.

In talking about his Vegas tenure with The Post earlier this season, Smith glowed about how it turned out to be so much better for his career than he expected. 

It was a slow start for Smith in New York, but that also was attributed to the team-wide struggles. In 58 contests with the Rangers, Smith collected 10 goals and 19 assists with average ice time of 15:36. 

Smith initially was brought in to fill in on the right wing of the top line next to Chris Kreider and Mika Zibanejad. 

That lasted just the first 10 games, and 25 total games this season. 

After he was a healthy scratch Nov. 30, Smith had some newfound jump to his game. 

“I’m not a believer that I took any positives out of it, to be honest,” Smith told The Post of his healthy scratch. “I know my game, I know when it’s going well, and I know when it’s not going well. When something like that happens, it’s tough for me personally. I don’t really have anything to say where, ‘Oh, that happened and now I’m a better player for it.’ I don’t believe that. But I think since the Christmas break, I’ve been playing better. I think our team is playing better. I just want to continue that trend. 

“I’m my biggest critic. Like I said, I know when I’m playing well, and I know when I’m not playing well. I know when I’m gripping my stick too tight, and I know when things are just very smooth. I don’t know how anyone wants to interpret it or take any spin on it.“I know the reality, and that’s how I approach every part of my game. If something isn’t working, I’m the one that’s going to make the change. No one else is going to.” 

The Rangers recalled defenseman Chad Ruhwedel from the Wolf Pack and subsequently returned Matthew Robertson to Hartford.