Question

lcm and hcf of the following integers by prime factorization method 8,9 and 25​

Answer 1

Step-by-step explanation:

2|8

2|4

2|2

|1 =>8=2×2×2

3|9

3|3

|1 =>9=3×3

5|25

5|5

|1 =>25=5×5

Hence there is no common divisior for all of them hence H.C.F. of 8,9 and 25 is 1 itself.

L.C.M. can be found by the following method

2|8,9,25

2|4,9,25

2|2,9,25

3|1,9,25

3|1,3,25

5|1,1,25

5|1,1,5

|1,1,1. Hence the least common multiple of 8,9 and 25 is 2×2×2×3×3×5×5 =>1800.

Hope it helps you.

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