#### Answer

84

#### Work Step by Step

Use the factor tree to find the prime factorization for each number:
2 and 3 are factors of 6. Both are prime. So, 2x3 is the prime factorization for 6.
4 and 3 are factors of 12. 3 is prime, but 4 is not. 2 and 2 are factors of 4. So, the prime factorization of 12 is 2x2x3.
7 is prime, so it can simply be circled.
Use each prime number the greatest number of times it appears in either numbers' prime factorization.
2 appears the most (2 times) in 12, 3 appears the same amount of times (1 time) in both 6 and 12, and 7 appears the most (1 time) in 7.
Therefore, the LCM is 2x2x3x7 which equals 84.