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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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The prime factorisation method for solving LCM and HCF for class 10th students. This is very important for class 10th board exam. How can i solve this question by best method. 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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1. (i) 12, 15 and 21

Writing the product of prime factors for all the three numbers, we get,

12=2Ã—2Ã—3

15=5Ã—3

21=7Ã—3

Therefore,

HCF(12,15,21) = 3

LCM(12,15,21) = 2 Ã— 2 Ã— 3 Ã— 5 Ã— 7 = 420

(ii) 17, 23 and 29

Writing the product of prime factors for all the three numbers, we get,

17=17Ã—1

23=23Ã—1

29=29Ã—1

Therefore,

HCF(17,23,29) = 1

LCM(17,23,29) = 17 Ã— 23 Ã— 29 = 11339

(iii) 8, 9 and 25

Writing the product of prime factors for all the three numbers, we get,

8=2Ã—2Ã—2Ã—1

9=3Ã—3Ã—1

25=5Ã—5Ã—1

Therefore,

HCF(8,9,25)=1

LCM(8,9,25) = 2Ã—2Ã—2Ã—3Ã—3Ã—5Ã—5 = 1800

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