1. **State the problem:** We need to find the lowest common multiple (LCM) of 154 and 273 using their prime factor trees. 2. **Prime factorization from the trees:** - For 154: $154 = 2 \times 7 \times 11$ - For 273: $273 = 3 \times 7 \times 13$ 3. **Formula for LCM using prime factors:** The LCM is found by taking the highest power of each prime factor appearing in either number. 4. **List all prime factors involved:** - From 154: 2, 7, 11 - From 273: 3, 7, 13 5. **Take the highest powers:** - 2 appears only in 154 - 3 appears only in 273 - 7 appears in both, take once - 11 appears only in 154 - 13 appears only in 273 6. **Calculate LCM:** $$\text{LCM} = 2 \times 3 \times 7 \times 11 \times 13$$ 7. **Multiply step-by-step:** - $2 \times 3 = 6$ - $6 \times 7 = 42$ - $42 \times 11 = 462$ - $462 \times 13 = 6006$ 8. **Final answer:** The lowest common multiple of 154 and 273 is **6006**.