Q. 34.4( 303 Votes )

# 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 :

Prime factors of any number is the representation of a number as a product of prime numbers it is composed of

for example: Prime factors of 20 = 2 x 2 x 5

HCF = Highest common factor = The product of the factors that are common to the numbers

LCF = Least Common Factor = Product of all the factors of numbers without duplicating the factor

(i)

let us write prime factors of the given numbers

12 = 2×2×3 = 2^{2}×3

15 = 3×5

21 = 3×7

Only 3 is common in all the three numbers, therefore

HCF = 3

As 3 is common in all three numbers, it will be taken as 1 time in the product of calculating LCM

LCM = 2^{2}×3×5×7 = 420

(ii) Let us write the prime factors of the given numbers

17 = 1×17

23 = 1×23

29 = 1×29

As only 1 is common from all the three factorsHCF = 1

As nothing except 1 is common from all three numbers, simply multiplying them will give LCM of numbers.LCM = 17×23×29 = 11339

(iii) Let us write the prime factors of the given numbers

8=2×2×2

9 = 3×3

25 = 5×5

As nothing is common in the numbersHCF = 1

As nothing is common in factors of numbers, numbers are simply multiplied to obtain LCMLCM = 2×2×2×3×3×5×5 = 1800

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