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Understanding GCF & LCM: Methods to Find the Greatest Common Factor and Least Common Multiple

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This guide provides a comprehensive overview of finding the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of numbers. Learn three methods to find the GCF of 28 and 42, including listing factors, creating area models, and using prime factorization. Additionally, discover how to determine the LCM of 39 and 52 through multiples and prime factorization techniques. With clear steps and examples, this resource simplifies these mathematical concepts for easier understanding and application.

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Understanding GCF & LCM: Methods to Find the Greatest Common Factor and Least Common Multiple

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  1. LCM & GCF

  2. GCF • Means Greatest Common Factor Or Largest Common Factor

  3. Find the GCF of 28 and 42 • There are at least three ways to do this: • Make a list of all factors for both numbers • Create an area model • Use prime factorization

  4. Make a list of all factors for both numbers (28, 42) a) Create all multiplication sentences that have a product of 28: {1 x 28, 2 x 14, 4 x 7, 7 x 4, 14 x 2, 28 x 1} b) Create all multiplication sentences that have a product of 42: {1 x 42, 2 x 21, 3 x 14, 6 x 7, 7 x 6, 14 x 3, 21 x 2, 42 x 1} c) Make a list of common factors: {1, 2, 4, 7, 14} d) Choose the largest (greatest) common factor (14) e) State the answer: “The GCF of 28 and 42 is 14”

  5. Create an area model (each square = 2 cm2 42 28

  6. Use the two numbers that you want to find the GCF for. • Build a rectangle with those dimensions • Find the largest square that will tile the rectangle (no gaps or overlaps) • State the answer

  7. Prime Factorization • Create the prime factorization for each number: 28 42 2 x 14 2 x 21 2 x 2 x 7 2 x 3 x 7 b) Circle pairs of common factors: 2 x 2 x 7 2 x 3 x 7 c) Create a multiplication sentence using ONLY common factors: 2 x 7 = 14 d) Write the answer: the GCF of 28 and 42 is 14

  8. LCM • Means Least Common Multiple or First (smallest) common multiple

  9. Find the LCM of 39 and 52 There are at least two ways to do this: • Make a list of multiples of each number • Use prime factorization

  10. Make a list ( LCM: 39,52) • Make a list of multiples: { 39, 78, 117, 156, 195, 234, 273, 312, 351, 390, 429, 468, 507, 546, 585, 624, …} {52, 104, 156, 208, 260, 312, 364, 416, 468, 520, 572, 624, 676, …} b) Look for common multiples: {156, 312, 468, 624, …} c) Find the smallest (least common multiple): 156 d) State the answer

  11. Use prime Factorization • Find the prime factors: 39= 3 x 13 52 = 2 x 2 x 13 b) Circle pairs of common factors: 3 x 13 2 x 2 x 13 c) Write a multiplication sentence that contains every unique prime factor and one of each common prime factor. or use all the factors, leave out the doubles: 2 x 2 x 3 x 13 = 156 d) The LCM of 39 and 52 is 156

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