Rashi points out an interesting fact about the threefold division (bold mine):
Le zent in O. F., the 100 (zuz weight). Menahem, however, connected it to the word מִנְיָן, a number (p. 118). We have here 240 “zuz,” [four zuz to a shekel]. From here we derive that the “maneh” of the Sanctuary was double, and they added a sixth to it in Ezekiel’s time, totaling 240 [zuz] (Men. 77a). When Scripture divided it into three parts and did not write simply, “sixty shekels shall the maneh be for you,” it commanded to make from it a weight one third of it, and a weight equaling a fourth of it, and a weight of the ordinary “maneh” as it was originally.
That is, the new mina within Ezekiel's vision is comprised of one-fourth, one-third, and one-whole of its original value.
Three Christian commentaries ranging from the 16th through the 18th centuries (Matthew Henry; John Gill; Jamieson, Fausset & Brown) inferred that Ezekiel's instruction in 45.12 is evidence of three denominations of currency.
For example, the JFB commentary, which also notes the fourth-third-whole as Rashi did, has the following (bold mine):
The standard weights were lost when the Chaldeans destroyed the temple. The threefold enumeration of shekels (twenty, twenty-five, fifteen) probably refers to coins of different value, representing respectively so many shekels, the three collectively making up a maneh. By weighing these together against the maneh, a test was afforded whether they severally had their proper weight: sixty shekels in all, containing one coin a fourth of the whole (fifteen shekels), another a third (twenty shekels), another a third and a twelfth (twenty-five shekels) [Menochius]. The Septuagint reads, "fifty shekels shall be your maneh."
In other words, the intention of this triple division was to prevent cheating the scales.