\(a\) and \(b\) are positive integers such that they do not have any common prime factor. What is the remainder when the

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\(a\) and \(b\) are positive integers such that they do not have any common prime factor. What is the remainder when the positive integer \(c\) is divided by the lowest number that has both \(a\) and \(b\) as its factors?

(1) \(c\) has the same number of factors as that of the least common multiple of \(a\) and \(b.\)

(2) When \(c\) is divided by \(4\) times the product of \(a\) and \(b,\) the remainder is \(0.\)

Answer: B

Source: e-GMAT