Chinese remainder theorem (two digit number)

Question

Find a two digit number that, when divided by $2,3,4,5$ gives remainder of $1,1,3,0$.

Can it be solved by chinese remainder theorem? How?

Answer 1

If $a$ is the number that gives $1,1,3,0$ when divided by $2,3,4,5$ then $a+5$ is divisible by $2,3,4,5$. Which means $a+5$ is divisible by $60$.

Answer 2

In order to use chinese remainder theorem all m must be pair-wise relatively prime that is co-prime with each other but now (2,4)=2 that is not coprimes so we co not use CRT Use onather methods