EL SEGUNDO, Calif. — The Lakers and Clippers are on the verge of playing each other for the first time ever in the playoffs.

On their end, the Lakers made sure they advanced to the Western Conference finals by eliminating the Houston Rockets with a 119-96 victory Saturday.

LeBron James had 29 points, Kyle Kuzma had 17, and the Lakers won their best-of-seven series, 4-1, taking four games in a row after losing the first one.

The series turned out to be a breeze as the Lakers drubbed the undersized Rockets in the post and short-circuited the high-flying Houston offense game after game.

The Lakers advanced to the Western Conference finals for the first time since 2010 after adding some stellar three-point shooting Saturday (19 of 37, 51.4 percent).

The Clippers aren’t quite there yet. Unlike the Lakers, they failed to close out their opponent after taking a 3-1 lead, falling to the Denver Nuggets after a lethargic fourth quarter Friday. Game 6 is Sunday.

It’s crazy to the think the two Los Angeles teams have never met in the post-season. The Lakers’ franchise has been around for 72 years, and the Clippers a mere 50.

The teams were close to seeing each other in the Western semifinals in 2006, but the Lakers lost in seven games to Phoenix in the first round. The Suns then beat the Clippers in the semifinals, which has been an issue for the Clippers over the years.

Dating all the way back to the franchise’s debut as the Buffalo Braves in 1970, the Clippers have never been past the conference semifinals. That could change soon.

The Lakers and Clippers, on another note, split this season’s series, 2-2. The Clippers won the first two, while the Lakers won the more recent ones, including a 103-101 victory when the league started up again July 30.

It’s tempting to think of a tussle between the Lakers’ two perennial All-Stars (James and Anthony Davis) and the Clippers’ duo (Kawhi Leonard and Paul George).

There’s also plenty of hardware among James (three championships) and Leonard (two titles).

With so much firepower on both starting units, the Western finals could come down to the reserves if the Lakers and Clippers play each other. The Clippers once held a clear-cut advantage, but the Lakers’ backups have had a strong playoff surge.

Kuzma was the hot hand off the bench Saturday, while Rajon Rondo was strong in the middle three games of the series. Alex Caruso was the Game 4 hero, scoring 16 points and drilling a game-clinching three-pointer in the final minute.

The Lakers did their part. It's up to the Clippers now.

Mike Bresnahan is the Lakers analyst for Spectrum SportsNet.