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

$a$ 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

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