To find the LCM of 58 and 64, we can use the prime factorization method. The LCM, or Least Common Multiple, of two or more numbers is the smallest value that all the numbers considered can be divided into evenly.

Here are the steps to find the LCM of 58 and 64:

1. Find the prime factorization of 58: 58 = 2 x 29
2. Find the prime factorization of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2
3. Identify the highest power of each prime factor that appears in either factorization. In this case, the prime factors are 2 and 29. The highest power of 2 is 6 (from 2 x 2 x 2 x 2 x 2 x 2), and the highest power of 29 is 1 (from 29).
4. Multiply the highest powers of each prime factor together: 2^6 x 29^1 = 1856

Therefore, the LCM of 58 and 64 is 1856.