The mother problem is:
Find the unit digit in LCM of $7^{3001} − 1$ and $7^{3001} + 1$
This problem comes with four options to choose the correct answer from,my approach,as the two number are two consecutive even numbers hence the required LCM is $\frac{(7^{3001} − 1)(7^{3001} + 1)}{2}$
Using algebra that expression becomes $\frac{(7^{6002} − 1)}{2}$,now it is not hard to see that unit digit of $(7^{6002} − 1)$ is $8$.
So the possible unit digit is either $4$ or $9$,As there was no $9$ as option I selected $4$ as the unit digit which is correct but as this last part is a kind of fluke I am not sure if my approach is right or not or may be I am unable to figure out the last part how to be sure that the unit digit of $\frac{(7^{6002} − 1)}{2}$ is $4$?