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LCM & GCF

LCM & GCF. GCF. Means Greatest Common Factor Or Largest Common Factor. 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. Make a list of all factors for both numbers (28, 42).

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LCM & GCF

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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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