Question 3 of 10intermediate🔧 ApplyNumerical6 marks

Find the LCM and HCF of the following integers by applying the prime factorisation method.

(i)

12, 15 and 21

Answer

HCF = 3, LCM = 420

(ii)

17, 23 and 29

Answer

HCF = 1, LCM = 11339

(iii)

8, 9 and 25

Answer

HCF = 1, LCM = 1800

Explanation

(i) 12 = 2² × 3, 15 = 3×53 \times 5, 21 = 3×73 \times 7. Common prime factor is 3. HCF = 3. LCM = 2² × 3×53 \times 5 × 7 = 420. (ii) All three numbers are prime with no common factors. HCF = 1. LCM = 17×2317 \times 23 × 29 = 11339. (iii) 8 = 2³, 9 = 3², 25 = 5². No common prime factors. HCF = 1. LCM = 2³ × 3² × 5² = 1800.

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