Summary 211 Section 3.2 Least Common Multiple Key Concepts The numbers obtained by multiplying a number by the whole numbers 1, 2, 3, and so on are called the multiples of the number. The least common multiple (LCM) of two given numbers is the smallest whole number that is a multiple of each given number. Using Prime Factors to Find the LCM of Two Numbers 1. Write each number as a product of prime factors. 2. The LCM is the product of unique prime factors from both numbers. Use repeated factors the maximum number of times they appear in either factorization. Writing Equivalent Fractions Use the fundamental principle of fractions to convert a fraction to an equivalent fraction with a given denominator. Ordering Fractions Write the fractions with a common denominator. Then compare the numerators. Examples Example 1 The numbers 5, 10, 15, 20, 25, 30, 35, and 40 are several multiples of 5. Example 2 Find the LCM of 8 and 10. Some multiples of 8 are 8, 16, 24, 32, 40. Some multiples of 10 are 10, 20, 30, 40. 40 is the least common multiple. Example 3 Find the LCM for the numbers 24 and 16. 24 2 2 2 3 16 2 2 2 2 LCM 2 2 2 2 3 48 Example 4 Write the fraction with the indicated denominator. 3 4 The fraction is equivalent to . Example 5 Fill in the blank with the appropriate symbol, < or >. The LCD is 36. 21 36 20 36 7 3 12 3 5 4 9 4 7 12 5 9 3 4 27 36 3 9 4 9 27 36 36 <
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