Voters went to the polls in Kansas, Michigan and Missouri yesterday to nominate Democratic and Republican candidates for the November elections.

In Kansas, first-term Gov. Mike Hayden narrowly won a Republican primary vote over real estate executive Nestor Weigand Jr., who tried to capitalize on voter anger over higher property taxes. On the Democratic side, former governor John Carlin trailed state Treasurer Joan Finney slightly in the first round of a comeback bid.

In Michigan, Republicans picked state Sen. John Engler over General Motors engineer John Lauve by 6 to 1 to challenge Gov. James J. Blanchard, and chose Rep. Bill Schuette 2 to 1 over lawyer Clark Durant to take on Sen. Carl Levin. Both Democratic incumbents are seeking third terms.

And in Missouri, Rep. Richard A. Gephardt, the House majority leader, easily won the Democratic nomination for an eighth term, claiming 82 percent of the vote against Nicholas F. Clement, a newspaper carrier who is a follower of political extremist Lyndon H. LaRouche.

Hayden, 51, led Weigand by 44 to 42 percent with 96 percent of the vote in, while four other opponents divided the remainder.

Weigand, 46, a Wichita businessman with no political experience, spent his own money lavishly in a 10-week television blitz to hit hard at Hayden's role in property reappraisal and implementing a new classification system that many blamed for big property tax increases in 1989. The changes were felt most by medium and small businesses.

On the Democratic side, Carlin, who served two terms in 1979-87, narrowly trailed longtime state Treasurer Finney 46 to 47 percent, while minister Fred Phelps had 7 percent.

Sen. Nancy Landon Kassebaum (R) piled up 87 percent of the vote against political unknown Gregory Walstrom in her bid for nomination to a third term. The Democratic Senate ballot listed political newcomer Dick Williams of Wichita and former representative Bill Roy, who tried to remove his name.

In Michigan, Schuette virtually ignored Durant in the GOP Senate primary, attacking Levin as too liberal. Similarly, Engler ignored his opponent in the GOP gubernatorial primary and concentrated on Blanchard, accusing the governor of using public relations gimmicks to obscure problems in Michigan's economy and budget.