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LCM and HCF

LCM and HCF. Understand what is meant by LCM and HCF C Give a number as a product of primes C Find LCM and HCF of sets of numbers B. Starter. Write down the prime numbers less than 50 What is the ONLY even prime? Why? Why is the number 1 NOT prime?

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LCM and HCF

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  1. LCM and HCF Understand what is meant by LCM and HCF C Give a number as a product of primes C Find LCM and HCF of sets of numbers B

  2. Starter • Write down the prime numbers less than 50 • What is the ONLY even prime? Why? • Why is the number 1 NOT prime? • Which of these are clearly NOT prime? Why? • 213 • 315 • 49721 • 2763 • 507

  3. Lowest Common Multiple • Write down the first 10 multiples of • 5 • 7 • 6 • 8 • What is the LCM of • 5 and 7 • 5 and 6 • 6 and 8

  4. Highest Common Factor • Write down the factors of • 30 • 56 • 40 • 21 • What is the HCF of • 30 and 40 • 30 and 56 • 21 and 40

  5. Using a factor tree 350

  6. What are the factors of 350? • 350 = 2 x 52 x 7 • Which of these must be factors and why • 25 • 20 • 14 • 15 • 70 • 50 • 125

  7. Write as a product of primes • 400 • 320 • 650 • 260 • 728 • 24 x 52 • 26 x 5 • 2 x 52 x 13 • 22 x 5 x 13 • 23 x 7 x 13

  8. Finding the HCF • Since 400 = 24 x 52 = 2 x 2 x 2 x 2 x 5 x 5 • 2 x 2 x 5 = 20 is a factor • Since 260 = 22 x 5 x 13 = 2 x 2 x 5 x 13 • 2 x 2 x 5 = 20 is a factor • Therefore 20 is a COMMON factor • Since I chose ALL the values they had in common, 20 is the Highest Common Factor

  9. What is the HCF of • 400 and 650 • 320 and 728 • 260, 650, and 728 • 260, 320, and 400 • 2 x 5 x 5 = 50 • 2 x 2 x 2 = 8 • 2 x 13 = 26 • 2 x 2 x 5 = 20

  10. Co - Prime • Some sets of numbers do not have prime factors in common • 35 = 5 x 7 • 52 = 2 x 2 x 13 • They still have a HCF • The HCF = 1 • These sets are Co-Prime

  11. Which of these sets are co-prime • 20 and 65 • 35 and 48 • 50 and 28 • 33 and 55 • 63 and 40 • 42, 30, and 35 • No (5) • Yes • No (2) • No (11) • Yes • Yes

  12. LCM • Explain why the LCM of 6 and 8 is NOT 48 • 400 x 650 = 260000 • Is 260000 a Common Multiple of 400 and 650? • Why? • Is it the LCM of 400 and 650? • Why? • What is?

  13. Ignoring the common factors • 650 = 2 x 5 x 5 x 13 • 728 = 2 x 2 x 2 x 7 x 13 • To find the LOWEST common Multiple we can ignore the factors repeated in the second number • LCM(650, 728) = 650 x 2 x 2 x 7 = 18200 • LCM(650, 728) = 650 x 728 ÷ 26 = 18200

  14. What is the LCM of • 320 and 650 • 260 and 728 • 400 and 320 • 20800 • 3640 • 1600

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