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Florida and Ohio are looking like friendly states for Donald J. Trump ahead of their primary elections next Tuesday, according to two new polls.

Surveys from CNN/ORC released on Wednesday show Mr. Trump with solid leads, potentially dealing serious blows to the campaigns of Senator Marco Rubio of Florida and Gov. John Kasich of Ohio. Both will face calls to quit the race if they fail to hold their home states.

In Florida, 40 percent of likely Republican voters support Mr. Trump, while 24 percent back Mr. Rubio. Trailing them are Senator Ted Cruz with 19 percent and Mr. Kasich with 5 percent.

Florida voters view Mr. Trump as being most fit to handle the economy, foreign policy and immigration. Mr. Cruz does better when it comes to social issues.

A separate poll released on Wednesday from Quinnipiac University shows an even steeper climb for Mr. Rubio in Florida, with Mr. Trump leading him by 23 percentage points.

In Ohio, Mr. Trump holds a smaller advantage over Mr. Kasich, topping him by a margin of 41 percent to 35 percent, according to CNN/ORC. Mr. Cruz comes in third with 15 percent, followed by Mr. Rubio at 7 percent.

Like Mr. Rubio in Florida, Mr. Kasich’s candidacy rests on a strong performance in Ohio. The poll shows him winning among women and holder voters. He is also seen as being better on social issues and more empathetic to the needs of voters.

Quinnipiac’s Ohio poll also shows Mr. Trump leading Mr. Kasich by 6 points, with the rest of the pack lagging far behind.

The surveys were conducted over the weekend while voters were going to the polls in other states and the outcomes could sway voters next week. CNN’s poll had a margin of error of plus or minus six percentage points, while Quinnipiac’s margin of error was plus or minus four percentage points.

On the Democratic side, CNN/ORC found that Hillary Clinton holds wide leads over Senator Bernie Sanders in both states. She tops him 63 percent to 33 percent in Florida and 61 percent to 34 percent in Ohio.

After pulling off a stunning upset in Michigan this week, Mr. Sanders will be looking to extend his momentum and demonstrate that he can defy the odds again.

Both Florida and Ohio are “winner-take-all” states. There are 165 delegates at stake for Republicans and 405 for Democrats.