On property of least common multiple to be a $D$-magic number

TL;DR

This paper investigates the property of least common multiple (lcm) as a D-magic number, showing that its least significant digit remains invariant across smaller bases, and extends this property to lcm+1.

Contribution

The paper demonstrates that lcm and lcm+1 possess the D-magic property, revealing a new invariant characteristic of these numbers across different numbering systems.

Findings

lcm has the D-magic property across bases

lcm+1 also preserves the D-magic property

Invariant least significant digit in smaller bases

Abstract

Least common multiple ($lcm$) has been shown to posses the property of $D$-magic number, that is, its least significant digit $0$ does not change when the number is transferred into all other numbering systems with smaller bases. The number $lcm + 1$ preserves this property as well.