Question 4 of 10intermediate🔧 ApplyNumerical6 marks

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i)

26 and 91

Answer

HCF = 13, LCM = 182 Verification: 13×18213 \times 182 = 2366 = 26×9126 \times 91

(ii)

510 and 92

Answer

HCF = 2, LCM = 23460 Verification: 2×234602 \times 23460 = 46920 = 510×92510 \times 92

(iii)

336 and 54

Answer

HCF = 6, LCM = 3024 Verification: 6×30246 \times 3024 = 18144 = 336×54336 \times 54

Explanation

(i) 26 = 2×132 \times 13, 91 = 7×137 \times 13. Common prime factor is 13. HCF = 13. LCM = 2×72 \times 7 × 13 = 182. (ii) 510 = 2×32 \times 3 × 5×175 \times 17, 92 = 2² × 23. Common prime factor is 2. HCF = 2. LCM = 2² × 3×53 \times 5 × 17×2317 \times 23 = 23460. (iii) 336 = 2⁴ × 3×73 \times 7, 54 = 2×32 \times 3³. Common prime factors are 2 and 3. HCF = 2×32 \times 3 = 6. LCM = 2⁴ × 3³ × 7 = 3024.

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