Each metal forms a single compound a chemist has a 0250g, Chemistry

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Each metal forms a single compound a chemist has a 0250g

Problem- All of the lanthanide metals (La through Lu, elements 57 through 71) reacts with HCl to form compounds having either the formula MCl2, MCl3 or MCl4 (where M represents the metallic element). Each metal forms a single compound. A chemist has a 0.250g sample of a lanthanide metal, and she wishes to identify the metal. She reacts the metal with excess HCl and obtains 0.427g of product. Based on this information, identify the metal and write the chemical formula of the product.

Please explain how you came up with answer I really want to understand how to calculate this

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Chemistry: Each metal forms a single compound a chemist has a 0250g

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