Story highlights Clinton holds a narrow lead in Ohio and a big edge in Pennsylvania

Voters are motivated by negative feelings toward their opponents

Washington (CNN) Hillary Clinton has pulled clearly ahead in Pennsylvania and holds a slight lead over Donald Trump in Ohio, but the two are in a tight race in the crucial battleground of Florida, according to new Quinnipiac University polls of likely voters in the key swing states show.

The results show the challenge facing Trump, who must compete in all three states to claim the 270 electoral votes he needs to defeat Clinton.

According to the polls, in Florida Clinton is at 46% to Trump's 45%. She leads 49% to 45% in Ohio and 52% to 42% in Pennsylvania.

It's the first time the polling outfit has surveyed likely voters -- rather than registered voters or all Americans -- in the 2016 election cycle, so the results can't be compared to previous Quinnipiac surveys.

With Libertarian Party nominee Gary Johnson and Green Party nominee Jill Stein added to the race, the equation doesn't change much.

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