Story highlights The Arizona victories handed enough delegates to Donald Trump and Hillary Clinton to help them maintain their leads in the delegate count despite victories from their primary competitors

Bernie Sanders won morale-boosting Democratic victories in Utah and Idaho while Ted Cruz came out on top in the Utah Republican caucuses

Washington (CNN) Donald Trump and Hillary Clinton notched convincing victories in Arizona, picking up the biggest prize on Western Tuesday that moved the front-runners ever closer to a general election clash.

The Arizona wins handed enough delegates to Trump and Clinton to help them maintain their leads in the delegate count despite victories from their primary competitors.

Photos: Who's running for president? Photos: Who's running for president? Ted Cruz, Donald Trump, John Kasich, Hillary Clinton and Bernie Sanders, Hide Caption 1 of 6 Photos: Who's running for president?



"So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement. Businessman Donald Trump announced June 16 at his Trump Tower in New York City that he is seeking the Republican presidential nomination. This ends more than two decades of flirting with the idea of running for the White House."So, ladies and gentlemen, I am officially running for president of the United States, and we are going to make our country great again," Trump told the crowd at his announcement. Hide Caption 2 of 6 Photos: Who's running for president?



"These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant." Sen. Ted Cruz of Texas has made a name for himself in the Senate, solidifying his brand as a conservative firebrand willing to take on the GOP's establishment. He announced he was seeking the Republican presidential nomination in a speech on March 23."These are all of our stories," Cruz told the audience at Liberty University in Virginia. "These are who we are as Americans. And yet for so many Americans, the promise of America seems more and more distant." Hide Caption 3 of 6 Photos: Who's running for president? Ohio Gov. John Kasich joined the Republican field July 21 as he formally announced his White House bid.



"I am here to ask you for your prayers, for your support ... because I have decided to run for president of the United States," Kasich told his kickoff rally at the Ohio State University. Hide Caption 4 of 6 Photos: Who's running for president?



"Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey." Hillary Clinton launched her presidential bid on April 12 through a video message on social media. The former first lady, senator and secretary of state is considered the front-runner among possible Democratic candidates."Everyday Americans need a champion, and I want to be that champion -- so you can do more than just get by -- you can get ahead. And stay ahead," she said in her announcement video. "Because when families are strong, America is strong. So I'm hitting the road to earn your vote, because it's your time. And I hope you'll join me on this journey." Hide Caption 5 of 6 Photos: Who's running for president?



"This great nation and its government belong to all of the people and not to a handful of billionaires, their super PACs and their lobbyists," Sanders said at a rally in Vermont on May 26. Sen. Bernie Sanders , an independent from Vermont who caucuses with Democrats, announced his run in an email to supporters on April 30. He has said the United States needs a "political revolution" of working-class Americans to take back control of the government from billionaires."This great nation and its government belong to all of the people and not to a handful of billionaires, their super PACs and their lobbyists," Sanders said at a rally in Vermont on May 26. Hide Caption 6 of 6

Bernie Sanders won morale-boosting Democratic victories in Utah and Idaho while Ted Cruz came out on top in the Utah Republican caucuses.

But the big win for Cruz was meeting the 50% threshold in Utah, according to a CNN projection, that hands him all of the state's 40 delegates. The Texas senator needed a win of that magnitude to avoid falling further behind Trump in the GOP delegate race.