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They have several applications.

To add, subtract, or just compare two fractions, you need to convert both fractions to a common denominator. The least common multiple is usually used, although any common multiple would work in this particular case (e.g., just multiplying the two denominators).

To simplify a fraction, you divide the numerator and the denominator by the same number. If you divide them by the greatest common factor, no further simplifications are possible.

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