Beautiful Liars

Louis gives one number of three digits abc\overline{abc}, to their students. They had the following conversation:

Alan:27\text{Alan}:27 divides abc\overline{abc}

Blas:11\text{Blas}:11 divides abc\overline{abc}


Jane:abc\text{Jane}:\overline{abc} is a divisor of 648,000648,000

Ronnie:abc\text{Ronnie}:\overline{abc} is a perfect square

Only three of this students told the truth. Find abc\overline{abc}.


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