BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:50 pm
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.
Answer:
D
Source: Manhattan prep
one
So, we have to find the least common multiple of x, 6 and 9. Note that 6 can be prime factorized as 2*3 and 9 can be prime factorized as 3 ^2;
So, the question is: What is the least common multiple of x, 2*3 and 3^2?
Let's take each statement one by one.
(1) The least common multiple of x and 6 is 30.
Note that 30/6 = 5, so the minimum value of x would be 5, and the maximum value would be equal to LCM = 30.
Whatever be the value of x, the LCM of x, 6 and 9 would be 90. Sufficient.
(2) The least common multiple of x and 9 is 45.
Again, note that the minimum value of x = 45/9 = 5, and the maximum value would be equal to LCM = 45.
So, values of x can be 5, 15, or 45.
Whatever be the value of x, the LCM of x, 6 and 9 would be 90. Sufficient.
Correct answer:
D
Hope this helps!
-Jay
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