How can greatest common factors and least common multiples help you work with fractions?

The greatest common factor (GCF) can help you reduce fractions. For example, 8/12 reduces to 2/3 because 8/12 = (2*4)/(3*4) = 2/3. Note the '4's in the numerator and denominator canceling. Also note that 4 is the GCF of 8 and 12.

The lowest common multiple (LCM) is used to get the lowest common denominator (LCD) which is needed to add or subtract fractions.

Example:

1/2 + 1/3 = 3/6 + 2/6 = (3+2)/6 = 5/6

The denominators 2 and 3 have an LCM of 2*3 = 6 (see note below), so the LCD is 6. Once all the denominators are the same, you add the numerators and place the result over the LCD.

Note: the multiplication trick only works if the GCF of the two denominators is 1. If the GCF is not 1, then you'll have to divide by the GCF.

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