EXHIBIT 32

The undersigned Chairman of the Board, President and Chief Executive Officer and Chief Financial Officer of Colgate-Palmolive Company each certify, pursuant to Rule 13a-14(b) under the Securities Exchange Act of 1934 and 18 U.S.C. § 1350, that:

(1)the Quarterly Report on Form 10-Q for the quarterly period ended June 30, 2020 (the “Periodic Report”) which this statement accompanies fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934; and

(2)information contained in the Periodic Report fairly presents, in all material respects, the financial condition and results of operations of Colgate-Palmolive Company.

Date: July 31, 2020

/s/ Noel R. Wallace

Noel R. Wallace

Chairman of the Board, President and

Chief Executive Officer

/s/ Henning I. Jakobsen

Henning I. Jakobsen

Chief Financial Officer