Yes.
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No, it is rational.
It is rational. It is rational. It is rational. It is rational.
The factors of 1845 are: 1, 3, 5, 9, 15, 41, 45, 123, 205, 369, 615, and 1845.The prime factors of 1845 are: 3, 5, and 41.
"Rational" is an adjective and so there cannot be "a rational" (and certainly not "an rational"). Any answer would depend on whether the question was about a rational number, a rational person, a rational argument or "a rational" combined with some other noun.
The LCM is 1845.