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Exercise State whether 51 is prime or composite. composite Exercise State whether 97 is prime or composite. prime Exercise Write the prime 2 2 • 3 •5 factorization of 90. Exercise Write the prime factorization of 150. 2 • 3 • 52 Exercise Find the greatest common factor of 90 and 150. 2 • 3 • 5 = 30 1x 2x 3x 4x multiples of 3 multiples of 4 3 4 6 8 9 12 12 16 5x 6x 7x 8x multiples of 3 15 18 21 24 multiples of 4 20 24 28 32 Least Common Multiple The least common multiple of two or more numbers is the smallest number that is a multiple of each of the given numbers. Example 1 List multiples to find the LCM of 10 and 12. 10: 10, 20, 30, 40, 50, 60, 70… 12: 12, 24, 36, 48, 60, 72, 84… The LCM of 10 and 12 is 60. Using Listing to Find the Least Common Multiple 1. List the multiples of each number. 2. Identify the first common multiple in each list of multiples. Example List multiples to find the LCM of 8 and 6. 24 Example List multiples to find the LCM of 15 and 36. 180 Using Exponential Form to Find the LCM 1. Write the prime factorization of each number in exponential form. Using Exponential Form to Find the LCM 2. Identify all the prime factors, both the common and different prime factors, that appear in the factorizations. Using Exponential Form to Find the LCM 3. Find the product of all the prime factors, using only the highest power of each that appears in any of the factorizations. Example 2 Find the LCM of 30 and 45. 30: 2 • 3 • 5 45: 3 • 3 • 5 = 32 • 5 LCM = 2 • 32 • 5 = 90 Example 3 Find the LCM of 12, 28, and 75. 12: 2 • 2 • 3 = 22 • 3 28: 2 • 2 • 7 = 22 • 7 75: 3 • 5 • 5 = 3 • 52 LCM = 22 • 3 • 52 • 7 = 4 • 3 • 25 • 7 = 2,100 Example Use prime factorizations to find the LCM of 40 and 50. 200 Example Use prime factorizations to find the LCM of 21 and 49. 147 Example Use prime factorizations to find the LCM of 32, 18, and 72. 288 Example Use prime factorizations to find the LCM of 42, 45, and 63. 630 LCM of 4x and 2 4x 2 3ab 2 5a b 3y 4z Example 4 Find the LCM of 15x3y and 21x2. 15x3y: 3 • 5 • x • x • x • y 21x2: 3 • 7 • x • x 3 • 5 • 7 = 105 x3 and y LCM = 105x3y Example Find the LCM of 12ab and 15b2c. 60ab2c Example Find the LCM of 63x2y3 and 72x3y4. 504x3y4 Example Find the LCM of 8mn2, 36m3n and 9m. 72m3n2 Example Find the LCM of 84r, 21s and 14t. 84rst Exercise Find the GCF and LCM of 36 and 48. GCF: 12; LCM: 144 Exercise Find the GCF and LCM of 12, 18, and 24. GCF: 6; LCM: 72 Exercise For any two numbers, what would be the least common factor? 1 Exercise For any two numbers, what would be the greatest common multiple? Exercise When you reduce fractions 350 such as , are you using 400 an LCM or a GCF? How? Exercise When you add fractions 1 1 7 such as 6 and 8 to get 24 , are you using an LCM or a GCF? How?