Question: Find the least common multiple of 8 and 12.
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- Since \( v \) is a positive multiple of 3, consider the multiples of 3 less than 14.14: 3, 6, 9, 12. These are the possible values for \( v \).
- Counting these values, we have: 3, 6, 9, 12 — a total of 4 values.
- Therefore, there are \(\boxed{4}\) possible values for \( v \).
- Solution: To find the least common multiple (LCM) of 8 and 12, we first determine their prime factorizations:
- = 2^3, \quad 12 = 2^2 \cdot 3^1
- The highest power of 2 is \( 2^3 \).
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