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WASHINGTON (AP) - US home prices rose in most major cities in October compared with a year ago, pushed up by rising sales and a decline in the supply of available homes. Higher prices show the housing market is improving even as it moves into the fall and winter, when sales traditionally slow.

The Standard & Poor's/Case-Shiller national index measuring prices in 20 cities rose 4.3 percent in October, up from a 3 percent annual gain in September.

Prices rose in October from a year ago in 18 of 20 cities. Phoenix led all cities with a 21.7 percent gain, followed Detroit, where prices increased 10 percent. Prices declined in Chicago and New York.

Prices fell in 12 of 20 cities in October compared with September. Monthly prices are not seasonally adjusted, so the decreases reflect the end of the peak buying season.