Two cousins visited jane today. one cousin visits every 42 days. the other visits every 429 days they will next visit on the same day in __ days? (answer 6006) how do you find the answer i need on that?

You need to find the lowest common multiple which is 6006 :)

The answer is the least common multiple of the number of days each cousin visits.
To find LCM, first find the prime factorization of the two numbers.

42=2*3*7
429=3*11*13

Next, create the prime factorization of the LCM with all of the factors from the original two numbers.
2*3*7*11*13=6006

You don't need to repeat the 3 even though it's in both prime factorizations because each number (of 42 and 429) can still be individually divided out of 6006 one factor at a time. If one of them had the same factor repeated more times than the other (say, your first number had three 3's in its prime factorization and your second number had only one), than you would need to include the greater number of repetitions (in the case of my example, three 3's would need to be in the prime factorization of their LCM).