The unit digit of $12^{12}$ is:

6

The correct answer is Option (4) → 6

Find the unit digit of $12^{12}$

Observe the pattern of unit digit of powers of 12:

12¹ → 2

12² → 4

12³ → 8

12⁴ → 6

12⁵ → 2 ... (pattern repeats every 4)

12 mod 4: 12 ≡ 0 mod 4 → position = 12 mod 4 = 0 → corresponds to 4th term in pattern

4th term in pattern = 6

Unit digit of 12¹² = 6