Six cards with digits 1, 2, 3, 4, 5, and 6 are on the table. Agnes made a six-digit number from these cards, divisible by six. Then she gradually removed the cards from the right. A five-digit number divisible by five remained on the table when she removed the first card. When she removed the next card, the four-digit number remained divisible by four. She obtained a successive three-digit number divisible by three and a two-digit number divisible by two. What six-digit number could Agnes originally have composed?
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