What is sucessive division to find a LCM?

Answer 1

Successive division, like factor trees, rainbows, fireworks, etc., is a way to notate the process of finding the prime factorization of a number. Once you have the prime factorizations, it's relatively easy to find the LCM.
Example: 30 and 42
Factor them.
30/2 = 15/3 = 5/5 = 1
2 x 3 x 5 = 30
42/2 = 21/3 = 7/7 = 1
2 x 3 x 7 = 42
Combine the factors, eliminating duplicates.
2 x 3 x 5 x 7 = 210, the LCM