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Low supply and high demand is driving home prices up across the nation, though this varies from market to market. identified five cities where prospective millennial home buyers have it especially tough.

San Jose, Calif. and Seattle, Wash. rank as the toughest markets for millennials, CNBC’s Diana Olick reports. Salt Lake City, Utah, Minneapolis, Minn., and Omaha, Neb., round out the top five. In all of these cities, millennials make up a higher share of the population and take home higher incomes than the U.S. median, according to Olick.

The inventory shortage is widespread, with the number of active listings this spring 8 percent lower compared with a year ago, while list prices are 8 percent higher. In the toughest cities, however, supply is nearly three times lower than in the rest of the nation. What is available is selling faster and bidding wars are pushing prices higher by about 14 percent.

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