Question

When \( 4^{157} \) is multiplied with \( 7^{113} \), what is the digit in the least significant place?

• A. 7
• B. 4
• C. 8
• D. 2

Hint:

Use unit digit cycles to quickly solve powers-related least significant digit questions.

Answer 1

The Correct Option is C

Step 1: Focus on unit digits
We are interested in the units digit (least significant digit) of: \[ 4^{157} \times 7^{113} \] Step 2: Units digit of \(4^n\)
The units digit of powers of 4 follows the cycle: 4, 6, 4, 6...
So, odd powers (like 157) have unit digit = 4.
Step 3: Units digit of \(7^n\)
The cycle of units digit of 7 is: 7, 9, 3, 1
Find \( 113 \mod 4 = 1 \Rightarrow \) first in cycle → units digit is 7.
Step 4: Final multiplication of unit digits
\[ 4 \times 7 = 28 \Rightarrow \text{units digit is } 8 \]