Prince George's County Executive Lawrence, J. Hogan told county school board members this week that they should cut their $281 million budget by $13 million-a reduction which, Hogan says, would increase class ssizes and could result in teacher layoffs.

The proposed 4.5 percent cut infuriated board members, and prompted a series of angry exchanges with each side accusing the other of political posturing.

The rhetoric marked the beginning of what will probably be the bitterest budget debate this year in Prince George's, which,for the first time, is operating under the severe constraints of the voter approved TRIM charter amendment.

Under present law, the school board is allowed to prepare its budget independently of the county, but Hogan can make general cuts in the board's proposed spending. If the county council approves the reductions, the school board must accept them.

Hogan knowledgeable officials say, is determined to push the school board into submitting to his funding priorities this year, while he is still three years from an election. Most board members are equally determined to stand their ground.

Hogan said yesterday that he had proposed a cut in the school board's salary budget that he hopes will force the board to renegotiate its tentative two-year contract with its 6,000-member teacher union. The contract agreement currently calls for salary increases of 5 percent in each of the next two years.

Board members said yesterday, however, that they intend to ratify the current contract in a meeting Thursday night, despite Hogan's cut. School Board Chairman Norman H. Saunders called Hogan's proposal "ludicrous" and "an insult."

"I'm not going to fund that contract," Hogan said. "If the school board wants to go back and negotiate (down) to 3 percent raises-which is what the other county employes are getting-then they can live within the budget I've proposed.

"otherwise, they are going to have to fire some teachers," Hogan said. "And I want it to be known that it will be the sschool board that will be firing teachers-not Larry Hogan. It's up to them."

"if teachers have to be fired," responded Saunders, "it will be Hogan's responsibility and Hogan's action. He's playing a political game, and he knows it."

Teachers have submitted their votes for the ratification of the proposed new contract, and a union official said yesterday the ballots would be tabulated today. If the teachers ratify the contract, as expected, the school board would be free to take action on it at its Thursday night meeting.

"I'm confident that the board will approve the contract," Saunders said.

In addition to salary cut, Hogan also will propose increasing class sizes by one pupil per class, transferring 129 school health aides to the health department for a $1.2 million reduction, and cutting 20 percent of the board's proposed $607,000 printing budget by merging the county and school printing services.

Hogan, who last week lambasted the school board for taking a county-financed trip to New Orleans, also will recommend that board members' travel and expense allocations be reduced a total of $18,000.

"The school board puts out a lot of propaganda at this time every year," Hogan said."But what is said about them is that they are expects in hiding pencils in their budget."

School board members said yesterday that they would not respond to most of Hogan's proposals, because, they said, Hogan had the authority only to make general reductions, not specific cuts.

The battle between Hogan and the school board ultimately will be decided by the county council. Council member Sue V. Mills said yesterday "the school board deserves" the cuts.

But council member Gerald T. McDonough said, "It's too early to tell what will happen. We will have to take a comprehensive look at the entire budget and see what else Hogan has put in it."