Question

Find the LCM and HCF of the following integers by applying the prime factorisation
method.
1) 12, 15 and 21 (ii) 17,23 and 29
(iii) 8, 9 and 25​

Answer 1

Step-by-step explanation:

(i)

12 = 2 x 2 x 3

15 =3 x 5

21 =3 x 7

HCF = 3

LCM = 2 x 2 x 3 x 5 x 7 = 420

(ii)

17 = 1 x 17

23 = 1 x 23

29 = 1 x 29

HCF = 1

LCM = 1 x 17 x 19 x 23 = 11339

(iii)

8 =1 x 2 x 2 x 2

9 =1 x 3 x 3

25 =1 x 5 x 5

HCF =1

LCM = 1 x 2 x 2 x 2 x 3 x 3 x 5 x 5 = 1800

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