I couldn't think of a concrete and simpler way, except for solving by using numbers. If we can find the value of x, we should be able to solve the problem.
statement 1 gives LCM of 30 ,so when cnosiderign the factors of 30, (1,2,3,5,6,10,15, 30). All the multiples of 5 can give LCM of 30. And when we substitue these multiples of 5 in the question, we always get LCM 90.
Applying the same logic for statement 2, we can find the LCM. So D the answer.
I would appreciate if there is a definite properties of LCM we could use instead of using numbers since it did take some to figure out the answer.
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GMAT Prep - LCM
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There's one thing you can learn about LCMs that makes this question quite easy:
to find the LCM of x, y, and z, you can first find the LCM of x and y, then find the LCM of this number with z.
That might sound confusing at first- the point is this: what is the LCM of 6, 8 and 10? You don't need to do it all at once. You can find the LCM of 6 and 8 first, which is 24, then find the LCM of 24 and 10 (which is 120). Or we could have found the LCM of 6 and 10 first (which is 30), then the LCM of 30 and 8 (again, we get 120). And so on.
Okay, on to the question:
The question asks, what is the LCM of x, 6 and 9.
From 1), the LCM of x and 6 is 30. By the discussion above, the question is just 'what is the LCM of 30 and 9?' Sufficient.
From 2), the LCM of x and 9 is 45. So the question is asking, 'what is the LCM of 45 and 6?'. Sufficient.
to find the LCM of x, y, and z, you can first find the LCM of x and y, then find the LCM of this number with z.
That might sound confusing at first- the point is this: what is the LCM of 6, 8 and 10? You don't need to do it all at once. You can find the LCM of 6 and 8 first, which is 24, then find the LCM of 24 and 10 (which is 120). Or we could have found the LCM of 6 and 10 first (which is 30), then the LCM of 30 and 8 (again, we get 120). And so on.
Okay, on to the question:
The question asks, what is the LCM of x, 6 and 9.
From 1), the LCM of x and 6 is 30. By the discussion above, the question is just 'what is the LCM of 30 and 9?' Sufficient.
From 2), the LCM of x and 9 is 45. So the question is asking, 'what is the LCM of 45 and 6?'. Sufficient.
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