3. Write down: $$ \begin{array}{ll} ext { a) the first fivo multiples of } 16 & ext { () the first sir prime numbers } \ ext { c) all the factors of } 18 & ext { d) the multiples of } 9 ext { between } 24 ext { and } 50 ext {. } \ ext { 4. Find the HCF and LCM for theso sets of numbers: }\end{array} $$

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3. Write down: $$ \begin{array}{ll}	ext { a) the first fivo multiples of } 16 & 	ext { () the first sir prime numbers } \ 	ext { c) all the factors of } 18 & 	ext { d) the multiples of } 9 	ext { between } 24 	ext { and } 50 	ext {. } \ 	ext { 4. Find the HCF and LCM for theso sets of numbers: }\end{array} $$

UpStudy AI · Accepted Answer

Below is one acceptable solution. We list the answers for question 3 parts first and then for question 4.

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3. Write Down:

a) The first five multiples of 16 are found by multiplying 16 by 1, 2, 3, 4, and 5:
  16 × 1 = 16  
  16 × 2 = 32  
  16 × 3 = 48  
  16 × 4 = 64  
  16 × 5 = 80  
Thus, the first five multiples are: 16, 32, 48, 64, 80.

b) The first six prime numbers are:
  2, 3, 5, 7, 11, 13.

c) All the factors of 18 are the numbers that divide 18 with no remainder. We have:
  1, 2, 3, 6, 9, 18.

d) The multiples of 9 between 24 and 50 are obtained by listing multiples of 9 and choosing those that lie between 24 and 50. Notice:
  9 × 3 = 27  
  9 × 4 = 36  
  9 × 5 = 45  
  9 × 2 = 18 (too low) and 9 × 6 = 54 (too high)  
Thus, the multiples are: 27, 36, 45.

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4. Find the HCF (Highest Common Factor) and LCM (Least Common Multiple) for each of these sets:

a) For the set of the first five multiples of 16: {16, 32, 48, 64, 80}

• HCF: Notice each number is a multiple of 16. In fact, 16 divides every one of these numbers. Hence, HCF = 16.
 • LCM: Write each as 16 × (1, 2, 3, 4, 5). The LCM is 16 times the LCM of {1, 2, 3, 4, 5}. Since LCM(1, 2, 3, 4, 5) = 60, we get LCM = 16 × 60 = 960.

b) For the first six prime numbers: {2, 3, 5, 7, 11, 13}

• Since all these numbers are prime (and distinct), they have no common factors other than 1. Thus, HCF = 1.
 • LCM: When numbers are pairwise relatively prime, the LCM is just the product. So LCM = 2 × 3 × 5 × 7 × 11 × 13 = 30030.

c) For the factors of 18: {1, 2, 3, 6, 9, 18}

• HCF: The common divisor of all these numbers is 1 (since not every number is divisible by any larger number). Thus, HCF = 1.
 • LCM: Because every number in the set divides 18, 18 is a common multiple. In fact, 18 is the least such number. Hence, LCM = 18.

d) For the multiples of 9 between 24 and 50: {27, 36, 45}

• Factor each number:
  27 = 3³  
  36 = 2² × 3²  
  45 = 3² × 5
  The common prime factor is 3, and the smallest power common to all is 3² = 9.
  Thus, HCF = 9.

• LCM: Take the highest powers among the factors:
  For 2: highest power is 2² (from 36).  
  For 3: highest power is 3³ (from 27).  
  For 5: highest power is 5¹ (from 45).  
  So LCM = 2² × 3³ × 5 = 4 × 27 × 5 = 540.

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Summary of Answers:

3.
 a) 16, 32, 48, 64, 80  
 b) 2, 3, 5, 7, 11, 13  
 c) 1, 2, 3, 6, 9, 18  
 d) 27, 36, 45

4.
 For {16, 32, 48, 64, 80}: HCF = 16, LCM = 960  
 For {2, 3, 5, 7, 11, 13}: HCF = 1, LCM = 30030  
 For {1, 2, 3, 6, 9, 18}: HCF = 1, LCM = 18  
 For {27, 36, 45}:    HCF = 9, LCM = 540

Any answer equivalent to the one above is correct.
3. a) 16, 32, 48, 64, 80 b) 2, 3, 5, 7, 11, 13 c) 1, 2, 3, 6, 9, 18 d) 27, 36, 45 4. a) HCF = 16, LCM = 960 b) HCF = 1, LCM = 30030 c) HCF = 1, LCM = 18 d) HCF = 9, LCM = 540

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