CAT 2023

Slot 1

QA

Question & Solution

Prime Factorising 1134, we get 1134 = $2\times\ 3^4\times\ 7$ and 168 = $2^3\times\ 3\times\ 7$

$1134^n$ is a factor of 168 => the factor of 2 should be atleast 3, for 168 to be a factor => n = 3.

Now, $1134^n$ = $1134^3=2^3\times\ 3^{12}\times\ 7^3$ is a factor of $168^m=\left(2^3\times\ 3\times\ 7\right)^m$ => m = 12 as power of 3 should be atleast 12.

=> So, m + n = 15.