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Numbers Properties • Learning Objective: Recognise and use multiples, factors, common factor, highest common factor, lowest common multiple and primes; find the prime factor decomposition of a number Must calculate the Lowest common Multiple of two numbers Should calculate the HCF for two numbers Could use HCF and LCM to add and subtract fractions with different denominators Key Words • Sequence, Term, nth term, consecutive, predict, rule, generate, continue, finite, infinite, ascending, descending, symbol, expression, algebra, integer, index, factors, multiples, square root, cube root, HCF, LCM Multiples A multiple of a number is found by multiplying the number by any whole number. What are the first six multiples of 4? To find the first six multiples of 4 multiply 4 by 1, 2, 3, 4, 5 and 6 in turn to get: 4, 8, 12, 16, 20 and 24. Any given number has infinitely many multiples. Multiples patterns on a hundred square The lowest common multiple The lowest 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, Multiples of 20 are : 20, 40, 60, 80, 100, Multiples of 25 are : 25, 50, 75, 100, 125, . . . The LCM of 20 and 25 is 100. 120, . . . WHY we need to know the lowest common multiple We use the lowest common multiple when adding and subtracting fractions. For example, Add together 4 9 and 5 . 12 The LCM of 9 and 12 is 36. 4 9 + ×4 ×3 5 16 12 ×4 = 36 ×3 + 15 36 = 31 36 Finding factors A factor is a whole number that divides exactly into a given number. Factors come in pairs. For example, what are the factors of 30? 1 and 30, 2 and 15, 3 and 10, 5 and 6. So, in order, the factors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30. The highest common factor What is the highest common factor (HCF) of 24 and 30? The factors of 24 are: 1 2 3 4 6 8 12 24 10 15 30 The factors of 30 are: 1 2 3 5 6 The highest common factor (HCF) of 24 and 30 is 6. Why do we need to know the highest common factor We use the highest common factor when cancelling fractions. For example, Cancel the fraction 36 . 48 The HCF of 36 and 48 is 12, so we need to divide the numerator and the denominator by 12. ÷12 36 48 = ÷12 3 4 Using prime factors to find the HCF and LCM We can use the prime factor decomposition to find the HCF and LCM of larger numbers. For example, Find the HCF and the LCM of 60 and 294. 2 2 3 5 60 30 15 5 1 60 = 2 × 2 × 3 × 5 2 3 7 7 294 147 49 7 1 294 = 2 × 3 × 7 × 7 Using prime factors to find the HCF and LCM 60 = 2 × 2 × 3 × 5 294 = 2 × 3 × 7 × 7 60 294 2 7 2 5 3 7 HCF 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 HCF and LCM Class Work • Frameworking Pupil Book 3 • Exercise 1b Page 5 Question 1-10 Extension if your really good.