The LCM of 30 and 42 is 210. There are different methods to find the LCM of two numbers, including prime factorization, division method, and listing the multiples. One way to find the LCM of 30 and 42 is to compare their prime factorizations and look for the highest power that each prime factor is raised to. The prime factorization of 30 is 2¹ x 3¹ x 5¹, and the prime factorization of 42 is 2¹ x 3¹ x 7¹. The LCM of 30 and 42 can be obtained by multiplying the prime factors raised to their respective highest power, which is 2¹ x 3¹ x 5¹ x 7¹ = 210. Another way to find the LCM of 30 and 42 is to list their common multiples and find the smallest one, which is also 210.