6:21. Use the fact that $3! = 3 \times 2!$ and $4! = 4 \times 3 \times 2!$ to factor out $2! + 4! + 5!$. You can do something similar with the other one.

6.22: Factor out each of the numbers using prime numbers and look at the prime numbers that were used (along with their exponents). The LCM will be the product of all the distinct prime numbers with the largest exponents you got in the prime factorizations.