Question

1. critique reasoning ron is trying to find the lcm of 4 and 6. his work is shown at the right. what is ron’s mistake? explain how to find the correct lcm of 4 and 6.

4: 2×2
6: 2×3
2×2×2×3 = 24, so the lcm of 4 and 6 is 24.

Explanation:

Step1: Analyze Ron's Work

Ron factored 4 as \(2 \times 2\) and 6 as \(2 \times 3\). To find LCM, we take the highest power of each prime factor. For prime 2, highest power is \(2^2\) (from 4), for prime 3, highest power is \(3^1\) (from 6). Ron used \(2^3\) (extra 2) which is wrong.

Step2: Calculate Correct LCM

Multiply highest powers: \(2^2 \times 3 = 4 \times 3 = 12\).

Answer:

Ron's mistake was using an extra factor of 2 (using \(2^3\) instead of \(2^2\)). The correct LCM of 4 and 6 is 12.