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## Adding and Subtracting Fractions

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**Chapter 3**Adding and Subtracting Fractions**Finding the Least Common Multiple Using Multiples**Method 1: Find the LCM of a List of Numbers Using Multiples of the Largest Number Step 1: Write the multiples of the largest number (starting with the number itself) until a multiple common to all numbers in the list is found. Step 2: The multiple found in Step 1 is the LCM.**Example**Find the LCM of 9 and 12. Write the multiples of 12 until we find a number that is also a multiple of 9. 12 1 = 12 Not a multiple of 9. 12 2 = 24 Not a multiple of 9. 12 3 = 36 A multiple of 9. The LCM of 9 and 12 is 36.**Finding the Least Common Multiple Using Multiples**Method 2: Find the LCM of a List of Numbers Using Prime Factorization Step 1: Write the prime factorization of each number. Step 2: For each different prime factor in step 1, circle the greatest number of times that factor occurs in any one factorization. Step 3: The LCM is the product of the circle factors.**Example**Find the LCM of 72 and 60. Circle the greatest number of prime factors found in either factorization. The LCM is the product of the circle factors.**Example**Find the LCM of 15, 18, and 54.**Writing Equivalent Fractions**To add or subtract unlike fractions, we first write equivalent fractions with the LCM as the denominator. To write an equivalent fraction, where a, b, and c are nonzero numbers.**Example**Write an equivalent fraction with the indicated denominator.**Example**Write an equivalent fraction with the indicated denominator.