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© Boardworks 20101 of 13 Unit 1 – Number Systems GCF and LCM

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© Boardworks 20102 of 13 Multiples of 6 Multiples of 8 2448 72 96 816324056648088104 … 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102… Common multiples

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© Boardworks 20103 of 13 Multiples on a hundred square

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© Boardworks 20104 of 13 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: Multiples of 20 are :20,40,60,80, 100, 120,... Multiples of 25 are : 25,50,75,100,125,... The LCM of 20 and 25 is100. 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.

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© Boardworks 20105 of 13 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 is40. What is the least common multiple (LCM) of 8 and 10? The least common multiple

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© Boardworks 20106 of 13 We use the least common multiple when adding and subtracting fractions. Add together 4 9 5 12 and. The LCM of 9 and 12 is 36. + 4 9 5 12 = 36 × 4 16 + 36 × 3 15 = 31 36 The least common multiple

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© Boardworks 20107 of 13 Common factor diagram

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© Boardworks 20108 of 13 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 is9.9. The greatest common factor

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© Boardworks 20109 of 13 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 is6.6. The greatest common factor

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© Boardworks 201010 of 13 We use the greatest common factor when simplifying fractions. Simplify the fraction. 36 48 The GCF of 36 and 48 is 12, so we need to divide the numerator and the denominator by 12. 36 48 = ÷12 3 4 The greatest common factor

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© Boardworks 201011 of 13 1 294 2 1 60 2 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. 302 153 55 60 = 2 × 2 × 3 × 5 1473 497 77 294 = 2 × 3 × 7 × 7 Using prime factors to find the GCF and LCM

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© Boardworks 201012 of 13 60 = 2 × 2 × 3 × 5 294 = 2 × 3 × 7 × 7 2 2 3 5 7 7 GCF of 60 and 294 =2 × 3= 6 LCM of 60 and 294 = 2 × 5 × 2 × 3 × 7 × 7 =2940 Using prime factors to find the GCF and LCM 60294

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© Boardworks 201013 of 13 Using prime factors to find the GCF and LCM

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