1. **State the problem:** We need to find the lowest common multiple (LCM) of 105 and 539 using their prime factor trees. 2. **Prime factorization from the trees:** - For 105: $105 = 3 \times 5 \times 7$ - For 539: $539 = 7 \times 7 \times 11 = 7^2 \times 11$ 3. **Formula for LCM:** The LCM of two numbers is found by taking the highest powers of all prime factors appearing in either number. 4. **Identify all prime factors and their highest powers:** - Prime factors: 3, 5, 7, 11 - Highest powers: - 3 appears as $3^1$ (only in 105) - 5 appears as $5^1$ (only in 105) - 7 appears as $7^2$ (since 7 appears squared in 539) - 11 appears as $11^1$ (only in 539) 5. **Calculate the LCM:** $$\text{LCM} = 3^1 \times 5^1 \times 7^2 \times 11^1 = 3 \times 5 \times 49 \times 11$$ 6. **Simplify step-by-step:** - $3 \times 5 = 15$ - $15 \times 49 = 735$ - $735 \times 11 = 8085$ 7. **Final answer:** The lowest common multiple of 105 and 539 is **8085**.