A method for obtaining an exhaustive set of multiplicative equations of relationship between the elements of an arbitrary set of the tested physical constants Cj in the form of their products in integer powers mj ranging from –N to N is proposed and used (calculations were performed for N = 2 and 4). A formal application of the proposed procedure reveals the minimum quanta of charge, mass, time, and distance and also a number of the relations describing the most general physical laws. It is shown that it is possible to construct a system of fundamental physical constants le, te, ee, me, α, and β (α is the fine-structure constant) with the simplest (m, s, kg, C) and zero dimensions to describe electromagnetic and gravitational interactions, as well as with the addition of Boltzmann’s constant (k), to describe the laws of thermal radiation. Planck’s constant (h), the speed of light in vacuum (c), electric (ε0), magnetic (μ0) and gravitational (G) constants are expressed through the revealed minimum quanta of length, time, charge, mass, and dimensionless constants. © 2023, The Author(s), under exclusive licence to Springer Nature Switzlerland AG.