American Motors Corp. reported yesterday that it lost $52.7 million in the first three months this year, making the January-to-March period the worst first quarter in the company's history.

The loss compared with a profit of $1.3 million (4 cents a share) in the 1980 first quarter. The previous record loss for the first quarter was $47.8 million in 1975.

First-quarter sales dropped 24 percent to $598 million from $795 million in the same period last year.

AMC's report was an indication that a sales slump continues to plague the nation's major automakers, which lost a total of $4.1 billion last year. In 1980, AMC lost a company record of $198 million.

Ford Motor Co. has said it expects to lose more in the first quarter of 1981 than it did in the last quarter of 1980, when it reported a $316 million deficit. Quarterly financial statements for industry leader General Motors Corp., Ford and Chrysler Corp. are expected later this month.

AMC said its combined worldwide auto and Jeep vehicle sales in the first quarter were 71,277, down 31 percent from 103,703 in the 1980 quarter.

"The auto recession has proved to be deeper and longer-lasting than anyone anticipated, and American Motors has been affected along with the rest of the industry," AMC Chairman Gerald C. Meyers said.

Meyers said the company had "implemented stringent economy measures, cut our salaried work force by more than 12 percent and eliminated all but necessary outlays."

Goodyear Tire & Rubber Co., meanwhile, said its first-quarter profits fell 14.9 percent to $43.1 million (59 cents a share) from $50.7 million (70 cents) a year ago as a result of a 56.8 percent decline in earnings from its foreign operations.

The nation's largest tiremaker said sales rose 9.6 percent to a record $2.2 billion from $2.0 billion a year ago.

U.S. profits nearly tripled to $24.8 million as domestic sales rose to $1.3 billion on stronger demand in the replacement-tire market.

American Express Co. reported a moderate gain in earnings for the first quarter but said high interest rates had hurt the company's performance.

Profits totaled $82 million ($1.14 a share), up from $78 million ($1.09) for the same quarter of 1980. Revenues were up 11 percent, from $1.29 billion to $1.43 billion.

Manufacturers Hanover Corp. holding company for the nation's fourth-largest commercial bank, reported a 6 percent increase in earnings for the first quarter, citing a rise in net interest income.

Manufacturers Hanover, whose principal subsidiary is Manufacturers Hanover Trust Co., said its earnings rose to $60 million ($1.79 a share) from $56.6 million ($1.70) in last year's first quarter. The company said its earnings were boosted $9.1 million because of a change in its method of accounting for depreciation of assets.

RCA Corp. said its first-quarter profits were down 47 percent from a year ago, primarily because of a nonrecurring gain of $36.6 million in 1980 and the costs of introducing its Videodisc system this year.

The company said it earned $41.9 million (33 cents a share) compared with $78.7 million (87 cents) in the first quarter of 1980. Revenues in the latest quarter totaled $1.95 billion, down 1 percent from $1.97 billion the previous year, RCA said.

Braniff International Corp. reported an operating profit of $454,000 for the first quarter, rebounding from a huge operating loss in last year's final quarter. But its latest results were far from spectacular.

Braniff, which is one of the nation's most financially distressed carriers, said its net results, including taxes and other considerations, showed a loss for the quarter of $24.7 million. In 1980's first quarter, Braniff had an operating loss of $22.5 million and a net loss of $21.9 million.

Braniff, based in Dallas, recorded a record $130 million loss for the 1980 fiscal year, and an independent financial study of the airline released earlier this week questioned whether it can avoid bankruptcy in the months ahead.

Polaroid Corp's first-quarter net income fell to $9.5 million (29 cents a share) from $17.4 million (53 cents) a year earlier as sales dropped 10 percent to $276.2 million from $308.3 million.