Question

find the lcm and HCF of the following by apply the prime a Factorisation method. 17,23 and 29 .
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Answer 1

Let us find the HCF of 17,23,29

17 = 17 × 1

23 = 23 × 1

29 = 29 × 1

∴ HCF (17,23,29) = 1

Let us find the LCM of17,23,29

LCM(17,23,29) = 17 × 23 × 29

∴ LCM(17,23,29) = 11339

Let us verify LCM and HCF is equals to the product of three numbers

LCM × HCF =17 × 23 × 29

17 × 23 × 29 × 1 =17 × 23 × 29

11339 = 11339

Answer 2

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Using prime factorisation method:

(i) 12, 15 and 21

Factor of 12=2×2×3

Factor of 15=3×5

Factor of 21=3×7

HCF (12,15,21)=3

LCM (12,15,21)=2×2×3×5×7=420

(ii) 17, 23 and 29

Factor of 17=1×17

Factor of 23=1×23

Factor of 29=1×29

HCF (17,23,29)=1

LCM (17,23,29)=1×17×23×29=11,339

(iii) 8, 9 and 25

Factor of 8=2×2×2×1

Factor of 9=3×3×1

Factor of 25=5×5×1

HCF (8,9,25)=1

LCM (8,9,25)=2×2×2×3×3×5×5=1,800