Why is 3 o’clock so important for practicing a devotion to Divine Mercy?

In the Gospels we are told that Jesus died at the ninth hour (cf. Mt. 27:46-50) on the Day of Preparation before Passover (cf. Mt. 27:62, John 19:14), which was also a Sabbath that year (cf. John 19:31). This sets the time of His Death as the ninth hour, (according to Sun time), or 3 p.m., on a Friday (since the Jewish Sabbath is Saturday). This is the Hour of Great Mercy, and the time which under the old covenant the Passover Lamb was slaughtered.

Can the Divine Mercy prayer be said at any time?

While 3:00 p.m. is the best time to pray the Divine Mercy Chaplet, the faithful can say this prayer any time of day and on any day of the week.