1. **Stating the problem:** Find the lowest common multiple (LCM) of 42 and 66 using their prime factor trees. 2. **Prime factorization of 42:** - 42 can be broken down into 2 and 21. - 21 factors further into 3 and 7. - So, the prime factorization is $$42 = 2 \times 3 \times 7$$. 3. **Prime factorization of 66:** - 66 breaks down into 2 and 33. - 33 factors further into 3 and 11. - So, the prime factorization is $$66 = 2 \times 3 \times 11$$. 4. **Finding the LCM:** - List the prime factors from both numbers, taking the highest power of each prime. - From 42 and 66, primes are 2, 3, 7, and 11. - The LCM is $$2 \times 3 \times 7 \times 11 = 462$$. 5. **Final answer:** The lowest common multiple (LCM) of 42 and 66 is $$462$$.