CAT 2023 Slot 1 Solved Paper

Prime Factorizing 1134, we get $1134=2\times 3^4\times 7$ and $168=2^3\times 3\times 7$
${1134}^{\mathit{n}}$ is a factor of $168\Rightarrow$ the factor of 2 should be atleast 3 , for 168 to be a factor $\Rightarrow \mathrm{n}=3$.
Now, ${1134}^{\mathit{n}}={1134}^3=2^3\times 3^{12}\times 7^3$ is a factor of ${168}^{\mathit{m}}={\left(2^3\times 3\times 7\right)}^{\mathit{m}}\Rightarrow \mathrm{m}=12$ as power of 3 should be atleast 12 .
⇒ So,$\mathit{m}+\mathit{n}=15$