VJesus12 wrote:If x is a positive integer, what is the least common multiple of x, 6 and 9?
(1) The least common multiple of x and 6 is 30.
(2) The least common multiple of x and 9 is 45.
We are given that x is a positive integer and need to determine the LCM of x, 6, and 9. If we can determine the value of x, then we can determine the LCM of x, 6, and 9.
Statement One Alone:
The least common multiple of x and 6 is 30.
Using the information in statement one, we see that x can be 5 since LCM(5, 6) = 30. However, x can be also 10, 15, or 30; any of these values of x would also make LCM(x, 6) = 30. This may seem insufficient to answer the question, but let's determine the LCM of x, 6 and 9 using these values:
If x = 5, LCM(5, 6, 9) = 90.
If x = 10, LCM(10, 6, 9) = 90.
If x = 15, LCM(15, 6, 9) = 90.
If x = 30, LCM(30, 6, 9) = 90.
Since the LCM of x, 6, and 9 is always 90 for all possible values of x, we see that statement one is sufficient to answer the question.
Statement Two Alone:
The least common multiple of x and 9 is 45.
Using the information in statement two, we see that x can be 5 since LCM(5, 9) = 45. However, x can be also 15 or 45; any of these values of x would also make LCM(x, 9) = 45. This may seem insufficient to answer the question, but let's determine the LCM of x, 6 and 9 using these values:
If x = 5, LCM(5, 6, 9) = 90.
If x = 15, LCM(15, 6, 9) = 90.
If x = 45, LCM(45, 6, 9) = 90.
Since the LCM of x, 6, and 9 is always 90 for all possible values of x, statement two alone is sufficient to answer the question.
Note: Using either statement, we've not determined a unique value for x. However, regardless what the value x is, we've determined a unique value for the LCM of x, 6 and 9.
Answer: D
