It's not that hard #LCM

LCM of first 100 natural numbers is $N$ . 101th natural number is 101. Therefore LCM of first 101 natural numbers is = LCM of $N$ and $101$ which is equal to $101N$ as 101 is a prime number and it has no factors in the first 100 natural numbers.

Similarly LCM of first 102 natural numbers is same as LCM of $101N$ and $102$ which is equal to $101N$ as 102 is a composite number and it's prime factors are 2, 3 and 17 which are all present in first 100 natural numbers.

103 is a prime number, so the LCM of first 103 natural numbers is $101N\cdot 103$ which is $10403N$ .

If we continue using this method, we find that all prime factors of 104 and 105 are present in first 100 natural numbers.

So the LCM of first 105 natural numbers is $10403N$ and value of $x$ is 10403.