Question

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

Answer 1

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12=2*2*3

15=3*5

21=3*7

HCF=3

LCM=2*2*3*3*5*7

=18*5*7*2

=90*7*2

=630*2

=1260

17=17*1

23=23*1

29=29*1

HCF=1

LCM=17*23*29

=11339

8=2*2*2

9=3*3

25=5*5

HCF=1

LCM=2*2*2*3*3*5*5

=8*9*25

=72*25

=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