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Unit 1 – Number Systems GCF and LCM

Unit 1 – Number Systems GCF and LCM. Common multiples. Multiples of 6. Multiples of 8. 12. 60. 6. 18. 54. 66. 102…. 24. 24. 48. 48. 96. 96. 72. 8. 16. 32. 40. 56. 64. 72. 80. 88. 104 …. 30. 42. 78. 90. 84. 36. Multiples on a hundred square.

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Unit 1 – Number Systems GCF and LCM

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  1. Unit 1 – Number SystemsGCF and LCM

  2. Common multiples Multiples of 6 Multiples of 8 12 60 6 18 54 66 102… 24 24 48 48 96 96 72 8 16 32 40 56 64 72 80 88 104 … 30 42 78 90 84 36

  3. Multiples on a hundred square

  4. The least common multiple The least common multiple (or LCM) of two numbers is the smallest number that is a multiple of both the numbers. We can find this by writing down the first few multiples for both numbers until we find a number that is in both lists. For example: 100, Multiples of 20 are : 20, 40, 60, 80, 120, . . . 25, 50, 75, 100, 125, . . . Multiples of 25 are : The LCM of 20 and 25 is 100.

  5. The least common multiple What is the least common multiple (LCM) of 8 and 10? The first ten multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80. The first ten multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. The least common multiple (LCM) of 8 and 10 is 40.

  6. The least common multiple 5 5 and . Add together 4 4 12 12 9 9 × 4 × 3 31 + = + 36 36 36 × 4 × 3 We use the least common multiplewhen adding and subtracting fractions. The LCM of 9 and 12 is 36. 16 15 =

  7. Common factor diagram

  8. The greatest common factor The greatest common factor (or GCF) of two numbers is the largest number that is a factor of both numbers. We can find the greatest common factor of two numbers by writing down all their factors and finding the largest factor in both lists. For example: Factors of 36 are : 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 45 are : 1, 3, 5, 9, 15, 45. The GCF of 36 and 45 is 9.

  9. The greatest common factor What is the greatest common factor (GCF) of 24 and 30? The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24. The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30. The greatest common factor (GCF) of 24 and 30 is 6.

  10. The greatest common factor 36 36 48 48 ÷12 ÷12 We use the greatest common factor when simplifying fractions. Simplify the fraction . The GCF of 36 and 48 is 12, so we need to divide the numerator and the denominator by 12. 3 = 4

  11. Using prime factors to find the GCF and LCM 2 60 2 294 1 1 We can use the prime factorization to find the GCF and LCM of larger numbers. Find the GCF and the LCM of 60 and 294. 2 30 3 147 3 15 7 49 5 5 7 7 60 = 2 × 2 × 3 × 5 294 = 2 × 3 × 7 × 7

  12. Using prime factors to find the GCF and LCM 60 = 2 × 2 × 3 × 5 294 = 2 × 3 × 7 × 7 60 294 2 7 2 3 5 7 GCF of 60 and 294 = 2 × 3 = 6 LCM of 60 and 294 = 2 × 5 × 2 × 3 × 7 × 7 = 2940

  13. Using prime factors to find the GCF and LCM

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