Veritas Official Explanation:
This abstract problem rewards students who have a good grasp on what it means for a number to be a least common multiple of two integers and who can easily use prime factorization to find least common multiples. Remember that the least common multiple of two integers can be constructed by first finding their prime factorizations and then combining those prime factorizations, using only the highest exponent to which each prime factor is raised.
Statement (1) gives that the least common multiple of x and y is 15. That means that their combined prime factorization is (3)(5). This does not tell you any information about the values of x and y, but (more importantly) it also gives no information about their relationship to z. You can therefore conclude that statement (1) is insufficient.
Statement (2) gives that the least common multiple of x and z is 18. This means that the combined prime factorization is (2)(32). Again, however, this gives no information about the relationship between x and z and the third variable, y, so statement (2) is insufficient.
Taken together, you know the relationship between x and y and the relationship between x and z. While this gives you no information about the actual values of any variable, the question is about the least common multiple, which only requires that you know 1) the prime factors of each number and 2) that for each prime factor you take the highest exponent for each. You should therefore recognize that the least common multiple of x,y and z can be made by combining the prime factorizations to get a least common multiple of (2)(\(3^2\))(5). Taken together, the two statements are sufficient and choice (C) is correct.
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