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Explanation:

168 = 2³ × 21 = 2³ × 3 × 7
1134 = 2 × 567 = 2 × 3⁴ × 7 

Now (1134)ⁿ = 2ⁿ × 34ⁿ × 7ⁿ 
Since 168 (2³ × 3 × 7) completely divides 1134_n (2ⁿ × 34ⁿ × 7ⁿ)
⇒ Power of 2 in 1134_n ≥ Power of 2 in 168
⇒ n ≥ 3
Similarly, we can check for power of 3 and power of 7 and we get the least value of n = 3.

Now (168)^m = 2^3m × 3^m × 7^m 
Since 1134ⁿ (2ⁿ × 3⁴ⁿ × 7ⁿ = 2³ × 3¹² × 7³) completely divides 168m (2^3m × 3^m × 7^m)
⇒ Power of 3 in 168^m ≥ Power of 3 in 1134ⁿ 
⇒ m ≥ 12
Similarly, we can check for power of 2 and power of 7 and we get the least value of m = 12.

∴ n + m = 3 + 12 = 15

Hence, option (c).