Los Angeles (CNN) -- Before Prince William and his wife, Catherine, left Los Angeles to return to London on Sunday, they got their hands dirty with paint and putty at a children's art center and shook hands with military veterans looking for work.

"On behalf of us both, how grateful we are to have been welcomed so warmly in the Golden State and City of Angels," Prince William said at the last stop of the royal couple's three-day Southern California visit.

A giant Union Jack flag and an equally large American flag served as the backdrop inside Sony Studios' sound stage 15 as Prince William addressed 1,500 military veterans, their spouses and recruiters from 150 companies Sunday afternoon. The cavernous building is where scenes for the "Wizard of Oz," "Spider Man" and many other movies were filmed.

William called the ServiceNation job fair "one of the seriously most important" of the many events during their 12-day North American tour.

"This is because it's about men and women, who with their own free will, choose to put their life on the line for their country," William said. "They are on the front line of a remarkable relationship between the United Kingdom, the United States and Canada, which has safeguarded our freedom for a century."

The problem of unemployment among former military families will "be raised monumentally by the Duke and Duchess of Cambridge being here," said U.S. Chamber of Commerce Vice President Kevin Schmiegel, one of the job fair organizers.

"Prince William is the most recognizable military officer in the world," Schmiegel said. "So, I think if they look at the portfolio of things that they're interested in raising awareness about, it makes sense that he is interested in this."

William said the job fair's mission is "very immediate and personal to us. Catherine and I both have friends back in Britain who could benefit from an initiative like this."

Earlier Sunday, William and Catherine spent an hour in Los Angeles' low-income Skid Row neighborhood with children at the Inner-City Arts Center. Each got their hands dirty creating their own art.

"What the hell is that?" William asked Catherine as he looked at her artwork. His wife was painting a snail as she sat among a group of fifth-graders.

"That's amazing," Catherine said to children as she admired their work in a ceramics class.

The royal newlyweds left a lasting impression at the center, literally. They each put their hands onto a board of putty, leaving ceramic imprints for future visitors to see.

Their whirlwind weekend in Southern California was designed to be a combination of commerce and charity missions for the royal couple.

Weekend events included the prince's participation in a polo competition in Carpinteria, California, on Saturday afternoon. Prince William and his team won the match after he scored four goals in the final game. His reward? A sterling silver and gold trophy along with a kiss by his wife.

Proceeds from the match go to a foundation supported by the prince and his brother, Harry, that helps disadvantaged youth, sustainable development and military families.

The royal couple has had a busy stay, which included a meeting with thespians and Hollywood's elite during an event by the British Academy of Film and Television Arts on Saturday night.

While Beverly Hills is the land of the famous, the visit by the recently married couple has caused a major stir.

Spago, Wolfgang Puck's restaurant, offered a British menu for the duration, including dishes served during the royal wedding festivities. The Beverly Hills eatery added Yorkshire pudding to its menu for the weekend.

Not to be outdone, the city's famously aggressive paparazzi tried to pursue the newlyweds at a private party at the British consul general's Hollywood home.

Neighbors near the residence, where the royals also spent the night, gave police permission to arrest photographers caught on private property.

The California visit ends the 10-day North American tour that began in Canada.

CNN's Michael Martinez contributed to this report.