(AP) -- Under a fresh cloud of overseas violence, Donald Trump and Hillary Clinton traded wins with their chief rivals on Tuesday and attacked each other's worldviews as the 2016 presidential contest turned into a clash of would-be commanders in chief.

While both front-runners scored victories in the night's biggest prize of Arizona, Democratic challenger Bernie Sanders won caucuses in Utah and Idaho and Republican Ted Cruz claimed his party's caucuses in Utah.

The victories kept Clinton and Trump from dominating another election night, but they both maintained a comfortable lead in the race for delegates that decide the presidential nominations.

Long lines and frenzied interest marked primary elections across the three Western states as the world grappled with a new wave of bloody attacks in Europe. The Islamic State group claimed responsibility for blasts in Brussels that left dozens dead and many more wounded.

"This is about not only selecting a president, but also selecting a commander in chief," Clinton said in Seattle as she condemned Trump by name and denounced his embrace of torture and hardline rhetoric aimed at Muslims. "The last thing we need is leaders who incite more fear."

Trump, in turn, branded Clinton as "Incompetent Hillary" as he discussed her tenure as secretary of state. "Incompetent Hillary doesn't know what she's talking about," the billionaire businessman said in an interview with Fox News. "She doesn't have a clue."

The back and forth between the front-runners came on a day when voters were eager to make their voices heard in the 2016 election.

In Utah, caucus-goers were dispatched by poll workers to local stores with orders buy reams of paper and photocopy fresh ballots amid huge turnout. The state Democratic Party's website crashed due to high traffic.

In Arizona, voters waited two hours or more in some places to cast primary ballots, while police were called to help control traffic.

As voters flooded to the polls, the presidential candidates lashed out at each other's foreign policy prescriptions, showcasing sharp contrasts in confronting the threat of Islamic extremism.

Clinton -- and Trump's Republican rivals -- questioned the GOP front-runner's temperament and readiness to serve as commander in chief, and condemned his calls to diminish U.S. involvement with NATO.

Addressing cheering supporters in Seattle, Clinton said the attacks in Brussels were a pointed reminder of "how high the stakes are" in 2016.

"We don't build walls or turn our back on our allies," she said. "We can't throw out everything we know about what works and what doesn't and start torturing people."

Cruz seized on Trump's foreign policy inexperience while declaring that the U.S. is at war with the Islamic State group.

"He doesn't have the minimal knowledge one would expect from a staffer at the State Department, much less from the commander in chief," he told reporters. "The stakes are too high for learning on the job."

The debate between the two took a detour late Tuesday night as they engaged in an unusual Twitter exchange about their wives.

The billionaire warned Cruz he would "spill the beans on your wife" after an anti-Trump group ran an ad in Utah featuring a picture of Trump's wife, Melania, from a photo shoot that ran in GQ magazine more than a decade ago.

Cruz shot back with a tweet of his own, saying in part, "Donald, if you try to attack Heidi, you're more of a coward than I thought."

Trump's brash tone has turned off some Republican voters in Utah, where Cruz claimed more than half of the caucus vote -- and with it, all 40 of Utah's delegates.

Yet that wouldn't make up for Trump's haul in Arizona, where he earned the state's entire trove of 58 delegates.

Trump supporter Easton Brady, 19, of Provo, Utah, cheered the billionaire's brash style, even as he acknowledged Trump doesn't play as well in Utah as other parts of the country.

"I think Trump says a lot of dumb things, but he's human," Brady said. "I don't care."

Arizona's win gives Trump a little less than half of the Republican delegates allocated so far. That's still short of the majority needed to clinch the nomination before the party's national convention this summer.

However, Trump has a path to the nomination if he continues to win states that award all or most of their delegates to the winner. Kasich was shut out for the night, leaving him with fewer delegates than Florida Sen. Marco Rubio, who quit the race last week.

Overall, Trump has accumulated 739 delegates, Cruz has 465 and Kasich 143. It takes 1,237 delegates to win the GOP nomination.

On the Democratic side, Clinton's delegate advantage is even greater than Trump's.

Coming off last week's five-state sweep of Sanders, the former secretary of state entered Tuesday leading by more than 300 pledged delegates. For the night, Sanders picked up at least 57 delegates to Clinton's 51, having won two states but losing Arizona. Less than two dozen delegates remain to be allocated, pending final vote tallies. Including superdelegates, Clinton was leading Sanders 1,681 to 927.

"These decisive victories in Idaho and Utah give me confidence that we will continue to win major victories in the coming contests," Sanders said in a statement.

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Associated Press writers Catherine Lucey in Everett, Washington, Jonathan Lemire in New York, Stephen Ohlemacher and Jill Colvin in Washington, Michelle Price in Orem, Utah, and Elliot Spagat in San Digeo contributed to this report.

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Follow Steve Peoples on Twitter at: http://twitter.com/sppeoples