1. **Problem statement:** Draw the prime factor tree for 190 and find the lowest common multiple (LCM) of 105 and 190. 2. **Prime factorization of 190:** - Start with 190. - Divide by the smallest prime factor: 2 (since 190 is even). - $190 \div 2 = 95$ - Next, factor 95. - 95 is divisible by 5: $95 \div 5 = 19$ - 19 is a prime number. So, the prime factor tree for 190 is: $$ 190 |\ 2 95 |\ 5 19 $$ 3. **Prime factorization summary:** - $105 = 3 \times 5 \times 7$ - $190 = 2 \times 5 \times 19$ 4. **Formula for LCM:** The LCM of two numbers is the product of the highest powers of all prime factors involved. 5. **Calculate LCM:** - Prime factors involved: 2, 3, 5, 7, 19 - Take the highest power of each: - 2 appears in 190 (power 1) - 3 appears in 105 (power 1) - 5 appears in both (power 1) - 7 appears in 105 (power 1) - 19 appears in 190 (power 1) So, $$\text{LCM} = 2 \times 3 \times 5 \times 7 \times 19$$ Calculate step-by-step: - $2 \times 3 = 6$ - $6 \times 5 = 30$ - $30 \times 7 = 210$ - $210 \times 19 = 3990$ 6. **Final answer:** The lowest common multiple of 105 and 190 is **3990**.