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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

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3,420, 1, 11339,1, 1800

33,1800, 23, 500 , 4, 7777

11, 339, 0, 220, 2, 8076

20,700, 5,907, 1, 2000

answer is A.

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Detailed Solution

(i) The numbers given in the first part are 12, 15 and 21. Here factor of 12, 15 and 21,

12 = 2 \times 2 \times 3

15 = 3 \times 5

21 = 3 \times 7

Here, 3 is common number in each factor. Thus,
H

ighest common factor, HCF (12, 15, 21) = 3

Now, lowest common factors of the number,

LCM (12, 15, 21) = 2 \times 2 \times 3 \times 5 \times 7 = 420

(ii) The numbers given in the second part are 17, 23 and 29. Here factor of 17, 23 and 29,

17 = 1 \times 17

23 = 1 \times 23

29 = 1 \times 29

So,

\begin{matrix} HCF (17, 23, 29) = 1 \\ LCM (17, 23, 29) = 1 \times 17 \times 23 \times 29 = 11, 339 \end{matrix}

(iii) The numbers given in the third part are 8, 9 and 25. Here factor of 8, 9 and 25,

8 = 2 \times 2 \times 2 \times 1

9 = 3 \times 3 \times 1

25 = 5 \times 5 \times 1

So,

\begin{matrix} HCF (8, 9, 25) = 1 \\ LCM (8, 9, 25) = 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 = 1, 800 \end{matrix}

Option 1 is correct.

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