EXHIBIT 32.1

              CERTIFICATION OF CHIEF EXECUTIVE OFFICER PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Wilfred J. Corrigan, certify pursuant to 18 U.S.C. Section 1350, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Quarterly
Report of LSI Logic Corporation on Form 10-Q for the quarterly period ended
September 28, 2003, fully complies with the requirements of Section 13(a) or
15(d) of the Securities Exchange Act of 1934 and that information contained in
such Form 10-Q fairly presents, in all material respects, the financial
condition and results of operations of LSI Logic Corporation.

                                       By: /s/ Wilfred J. Corrigan
                                           ------------------------------------
                                       Name:  Wilfred J. Corrigan
                                       Title: Chairman & Chief Executive Officer