$=79$, Find the maximum value of the volume of this rectangular prism.



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【Solution】Solution: According to the analysis, $\overline{\mathrm{ab}}+\overline{\mathrm{bc}}=79, b+c \neq 19$, so $b+c=9, a+b=7$,
(1) $b+c=4+5$, then $a=2, b=5, c=4$ or $a=3, b=4, c=5$,

The larger volume is: $3 \times 4 \times 5=60$;
(2) $a+b=3+4$, then $a=3, b=4, c=6$ or $a=4, b=3, c=6$,

The larger volume is: $3 \times 4 \times 6=72$;
In summary, the maximum volume of the rectangular prism is: $a \times b \times c=3 \times 4 \times 6=72$.
Therefore, the answer is: 72.