By winning Michigan, Mississippi and Hawaii, Donald Trump captured the greatest share of the 150 Republican delegates at stake Tuesday and gained momentum as the race heads toward the March 15 votes.

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Donald Trump drew closer to grasping the Republican presidential nomination with his victories in three states Tuesday night, and the chances of party leaders’ wresting it from his hands at a contested convention were a bit more remote Wednesday.

By winning Michigan, Mississippi and Hawaii, Trump captured the greatest share of the 150 delegates at stake Tuesday, and his mathematical path to a majority of 1,237 delegates needed to secure the nomination is increasingly brighter than his rivals. He needs about 54 percent of outstanding delegates; his closest rival, Sen. Ted Cruz of Texas, needs 62 percent.

But Trump gained something even more valuable than delegates Tuesday: momentum as the race heads into a watershed moment, March 15, when the first states that award delegates winner-take-all hold their primaries. They include Sen. Marco Rubio’s home state, Florida, and Gov. John Kasich’s, Ohio. Both men have their backs to the wall, fighting for their political lives.

“After Florida and Ohio,” said Barry Bennett, a senior adviser to Trump, who is closely tracking the delegate race for him, “if we win both those states, Cruz will be 300 delegates behind. The winner-take-all states are the rocket fuel.”

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Cruz did better than polls predicted in Michigan and Mississippi, and he won a commanding victory in Idaho. In all, he netted an estimated 57 delegates to Trump’s 71.

But Cruz, who trails Trump in delegates awarded so far by an estimated 462 to 358, is facing a primary map of big states in the North and West that are demographically more favorable to Trump. He seemed to acknowledge the difficulty of overtaking Trump before the convention even if the race becomes the two-man contest he has long sought.

“Look, Reagan and Ford battled it out in a contested convention,” Cruz told Fox News. “That’s what conventions are for.”

Kasich’s third-place finish in Michigan, a blow after he predicted as late as Tuesday night that he would come in second, is a sign of potential trouble for him in Ohio because of the demographic similarity of the two states.

Kasich’s chief strategist, John Weaver, sought to make the case that the governor was in a good position as the nominating race moves away from the South.

“After March 15, more than 1,000 delegates will still be available, and the electoral map shifts significantly in our favor, with the delegate-rich states fitting Governor Kasich’s profile,” Weaver wrote in a strategy memo late Tuesday.

But even if Kasich wins Ohio and its 66 delegates, along with some of the others at stake on the same day in Illinois, Missouri and North Carolina, his chances of gaining a majority of 1,237 is close to a mathematical impossibility. Only 1,000 delegates will remain after March 15.

“His path to the nomination during regulation time, primary season, is narrow enough to be invisible,” said Joshua Putnam, a political-science lecturer at the University of Georgia.

Similarly, Rubio is facing a daunting mathematical roadblock. In failing to reach 15 percent of the votes in Michigan and Mississippi, and 20 percent in Idaho, he was shut out of delegates entirely in the three states holding primaries Tuesday. He may have picked up as few as two in Hawaii.