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Which choice shows how to find the least common multiple of 9 and 42 through prime factorization?
9 ⟶ 3 × 3
42 ⟶ 2 × 3 × 7
LCM: 2 × 3 × 3 × 7 = 126
9 ⟶ 3 × 3
42 ⟶ 2 × 3 × 7
LCM: 3 × 3 × 2 × 3 × 7 = 378
9 ⟶ 3 × 3
42 ⟶ 2 × 3 × 7
LCM: 3
9 ⟶ 3 × 3
42 ⟶ 2 × 3 × 7
LCM: 2 × 3 × 7 = 42
The correct choice is:
9 ⟶ 3 × 3
42 ⟶ 2 × 3 × 7
LCM: 2 × 3 × 3 × 7 = 126
Explanation: To find the least common multiple (LCM) using prime factorization, you take each prime factor from both numbers at their highest power. In this case, we include 2 (from 42), 3 (the highest power is (3^2) from 9), and 7 (from 42). So, the LCM is calculated as (2^1 × 3^2 × 7^1 = 2 × 3 × 3 × 7 = 126).