What is the \(LCM\) of \(x\) and \(12?\)
(1) The Least Common Multiple of \(x\) and \(9\) is \(45?\)
(2) The Least Common Multiple of \(x\) and \(4\) is \(20?\)
[spoiler]OA=B[/spoiler]
Source: Manhattan GMAT
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What is the \(LCM\) of \(x\) and \(12?\)
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terminator12
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Statement 1:
45 = \({3^2}\)*5
9 = \({3^2}\)
Hence, x = 5*\({3^a}\)
where a = 0, 1 ,2
x can be 5, 15, 45
Hence, this statement is insufficient.
Statement 2:
20 = \({2^2}\)*5
4 = \({3^2}\)
Hence, x = 5*\({2^a}\)
where a = 0, 1 ,2
x can be 5, 10, 20
Hence, this statement is insufficient.
Combining both statements, we get x = 5
Hence, answer should be C.
45 = \({3^2}\)*5
9 = \({3^2}\)
Hence, x = 5*\({3^a}\)
where a = 0, 1 ,2
x can be 5, 15, 45
Hence, this statement is insufficient.
Statement 2:
20 = \({2^2}\)*5
4 = \({3^2}\)
Hence, x = 5*\({2^a}\)
where a = 0, 1 ,2
x can be 5, 10, 20
Hence, this statement is insufficient.
Combining both statements, we get x = 5
Hence, answer should be C.
