Sears, Roebuck & Co., the nation's largest retailer, took a major step toward its goal of becoming a major financial services firm today by announcing its intention to acquire Los Angeles-based Coldwell, Banker & Co., one of the nation's biggest real estate companies.

Sears began buying Coldwell, Banker stock in 1978 and today owns nearly 900,000 shares, about 17.6 percent of the 5.1 million outstanding. Sears said it would pay $42 a share cash for 1.536 million shares of Coldwell's stock and eventually exchange Sears stock for the rest. Sears said it might pay cash for as many as 2.3 million shares, if the larger purchase would not affect the tax-free nature of the deal.

Coldwell, Banker closed at $23.75 a share Friday. Today, its stock soared (trading was halted on the New York Stock Exchange and elsewhere until about 1 p.m. because of the merger announcement) to $39.875. Sears dropped a quarter to $16.25.

Boards of directors of both companies have approved the merger in principle.

Officials of A.E. Le Page Ltd., the big Toronto real estate services firm that owns about as many shares of Coldwell as Sears does, did not comment on the proposed merger. Le Page, Canada's largest real estate company, has been interested in acquiring Coldwell too, industry sources said.

A spokesman for Le Page said the company would not comment until it had "full details" on the Sears offer and until Sears files its offer to buy Coldwell stock, which the giant Chicago retailer said it would do by Friday. Le Page Chairman Gordon C. Gray is a member of Coldwell's board of directors.

Sears, which last year had $25.2 billion in sales, already is well on its way to becoming a major financial services firm, offering a broad spectrum of products to consumers.

The company owns Allstate Insurance Co., one of the nation's biggest, a California savings and loan association with assts of $2.3 billion, and already has a real estate arm, The Seraco Group. Seraco is a major developer of shopping centers and office buildings -- business in which Coldwell Banker is also active.

The company announced recently that it plans to set up a money market mutual fund.

Sears Chairman Edward Telling said Coldwell would become part of the Seraco group and that Coldwell Chairman C.W. Poulson would head Seraco. Preston Martin, the former chairman of the Federal Home Loan Bank Board who has been head of Seraco, will become a special assistant to Telling, a Sears spokesman said.

Last year Sears generated $18.7 billion from merchandising, $6.2 billion from Allstate and $420 million from Seraco. Coldwell Banker last year year had revenues of $345 million.

Although Coldwell offers a broad spectrum of real estate services -- from mortgage banking to shopping centers to property management -- its biggest single activity is real estate brokerage, according to Vice President William O. Hinkley. It had been agressively acquiring large real estate firms in major metropolitan areas until this year's downturn in the housing market. Coldwell has had operations in the Washington area since 1976, when it bought the Alexandria-based Routh Robbins Realtors and set up a separate commerical brokerage office.

In recent years a number of American companies have broadened the financial services they offer in an attempt to attract more and more customer dollars. Merrill Lynch & Co., the nation's largest brokerage firm, already is a major factor in the real estate, executive relocation and insurance fields. This year Prudential Insurance Co., the nation's largest insurer, bought The Bache Group Inc., the country's eighth-biggest broker; American Express Co. bought Shearson Loeb Rhoads, the second-biggest broker.