)what is the last digit (i. e., the least significant digit) of 34001?

The 3. For example, if I wrote 00034001, the number is the same, but it is preceded by three unnecessary zeroes. However, if I wrote 34001000, it is a very different number. That’s why 3 is your answer.

The digit 1 is the least significant digit.

The higher the place value, the higher the significance of the digit.
The digit 3 stands for 30 000 and the digit 4 stands for 4000. 
⇒ The digit 3 is more significant than the digit 4

The digit 4 stands for 4000 and digit 1 stands for 1.
⇒ The digit 4 is more significant than the digit 1.

The digit 1 is the least significant digit.