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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

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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

by Gmat_mission » Wed Feb 23, 2022 8:53 am

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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 $$0.$$