Prime Factorizing 1134, we get 1134=2×34×7 and 168=23×3×7 1134n is a factor of 168⇒ the factor of 2 should be atleast 3 , for 168 to be a factor ⇒n=3. Now, 1134n=11343=23×312×73 is a factor of 168m=(23×3×7)m⇒m=12 as power of 3 should be atleast 12 . ⇒ So,m+n=15