Mitt Romney won the Kentucky Republican presidential primary Tuesday, inching closer to the GOP nomination for president.

With no serious opposition left, the former Massachusetts governor easily won the contest, claiming at least 32 of the 42 delegates at stake in Kentucky. Voters also went polls in Arkansas, with 33 delegates at stake in that state.

Romney could win all of Kentucky's delegates, though Texas Rep. Ron Paul, who stopped actively campaigning last week, was hovering just below 15 percent of the vote in early returns. That's the threshold needed to win delegates in Kentucky.

Romney has 1,024 delegates, leaving him 120 shy of the 1,144 delegates needed to win the GOP nomination for president. If he continues to dominate, he will reach the magic number next week, when voters in Texas go to the polls.

Virtually assured of the party nod, Romney has been in general election mode for weeks. He's been spending much of his time fundraising and focusing on Democratic President Barack Obama.

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As voters in the two Southern states weighed in, Romney planned to spend Tuesday evening at a campaign fundraiser in New York before an appearance Wednesday in Washington to deliver a speech.

He is in the midst of a three-day swing through the Northeast that is expected to bring in at least $10 million.

Romney has struggled in some previous Southern contests, when former Pennsylvania Sen. Rick Santorum and former House Speaker Newt Gingrich were in the race. With them on the sidelines, Romney has an opportunity to display solid support in two states he should win in November.

Even though they have left the race, Santorum, Gingrich and Paul were on the ballot in Kentucky and Arkansas.

Texas, which offers 152 delegates, votes May 29.