The LCM of 2, 4, 6, 8, 10, and 12 is 120. Let's see how we can get the LCM by prime factorization.
First, determine the prime factors of all the numbers:
2: 21
4: 2 × 2 = 22
6: 2 × 3 = 21 × 31
8: 2 × 2 × 2 = 23
10: 2 × 5 = 21 × 51
12: 2 × 2 × 3 = 22 × 31
Find the highest power of each prime number and multiply them together:
23 × 31 × 51 = 120