Salt Lake-based American Stores Co. made a surprise but "friendly" $1.72 billion tender offer Tuesday for California-based Lucky Stores Inc., a merger that would create the nation's largest chain of supermarkets by combining third-largest American and fourth-largest Lucky.

Under the proposal, American's chain of Alpha Beta stores would become Lucky Stores and the Alpha Beta headquarters would move from Salt Lake City to Dublin, Calif., where the Lucky headquarters are located.Lucky operates supermarkets and food centers in the West, Midwest and Southwest, principally in California and Arizona. American operates supermarkets and drug stores nationwide.

In a letter to Lucky Stores chairman John M. Lillie, American Stores chairman L.S. Skaggs said American will "promptly commence" a cash tender offer of $45 per share for all 38.44 million shares of Lucky Stores stock.

Shares in Lucky Stores immediately rose $14.25 to $46.50 higher than the American Stores bid apparently on the assumption that a higher offer will be forthcoming.

Shearson Lehman Hutton Inc. is acting as the company's financial adviser and dealer manager in the offer.

The two companies have combined sales of about $21 billion, a figure that would place the merged entity ahead of Safeway stores as the nation's largest a lead that would likely lengthen considering the faster growth rate of American and Lucky over Safeway, which was recently taken private.

Skaggs said Americanintends to combine its existing Alpha Beta stores with Lucky's operation and operate the merged chain under the Lucky name, "utilizing Lucky's business philosophy, including pricing and marketing strategies."

Skaggs said he hopes Lucky's existing management personnel and the existing Lucky Stores board of directors will remain with the merged company. To further that, Skaggs said the new company will make its headquarters in Dublin, not Salt Lake City.

While Lucky Stores had no immediate comment on the offer, a spokesman did point out that Lucky shareholders should be aware that its certificate of incorporation includes a provision that limits the voting power of any shareholder of more than 10 percent of the company's shares.

Specifically, each share held in excess of 10 percent is entitled to one one-hundredth of a vote and in no case may a shareholder with more than 10 percent cast more than 15 percent of the total votes on any given issue.

This "poison pill" was enacted nearly two years ago when Lucky Stores successfully fended off a hostile $37-per-share takeover attempt by New York investor Asher Edelman by buying back some of its shares and by divesting some of its non-food subsidiaries. The provision is due to expire Dec. 22 but may not be waived by the board, according to the corporate bylaws.

In his letter to Lucky chairman Lillie, Skaggs acknowledged that problems may arise relating to antitrust violations if the merger is completed because both Lucky and American compete heavily in Western states. Government regulators might force some holdings of the merged company to be divested.

" . . . Certain questions may therefore arise under applicable antitrust laws," said Skaggs. "We are willing to take all necessary steps to be in full compliance with such laws. We seek your cooperation in this regard in order that such actions may be considered on a coordinated basis and implemented efficiently and expeditiously so that your shareholders may promptly receive the full and fair value of their . . . shares."