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Is this algebra statement not nice?

Source: Kyiv City MO 2024 Round 1, Problem 10.5/11.4

January 28, 2024
algebra

Problem Statement

Find the smallest real number MM, for which {a}+{b}+{c}M\{a\}+\{b\}+\{c\}\leq M for any real positive numbers a,b,ca, b, c with abc=2024abc = 2024. Here {a}\{a\} denotes the fractional part of number aa.
Proposed by Fedir Yudin, Anton Trygub