Difference of LCMs

To find the LCM of the numbers from $1$ to $53$ , we must find all largest $p^{n}$ below $53$ , where $p$ is a prime number, and multiply them. The same goes with the other sequence of numbers but all $p^{n}$ must be below $58$ .

List of prime numbers: $\begin{array}{cccccc} 2 & 3 & 5 & 7 & 11 & 13 \\ 17 & 19 & 23 & 29 & 31 & 37 \\ 41 & 43 & 47 & 53 & 59 & ... \end{array}$

The list above shows that the prime numbers from $53$ below and from $58$ below are the same. There are also no $p^{n}$ that is between $53$ and $58$ , meaning the factors to make their LCMs are the same. Thus, their LCMs have a difference of $\boxed{0}$ .