(Solved) Find the LCM and HCF Of the following integers by applying the prime factorisation method. 1) 12,15 and 21 2) 17,23 and 29 3) 8,9 and 25

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 QUESTION :-

Find the LCM and HCF Of the following integers by applying the prime factorisation method. 

1) 12,15 and 21

 2) 17,23 and 29 

3) 8,9 and 25


ANSWER :-

1) 12,15 and 21

Product of prime factor

12=2×2×3 = 2² × 3

15=3×5

21=3×7

Here, 3 is common among 12,15 and 21

SO, HCF(12,15,21) = 3


In LCM we have to multiply all number with highest power but number should not be repeated. 

LCM(12,15,21)= 2² × 3¹ × 5¹ × 7¹ = 420


2) 17,23 and 29


17=1×17

23=1×23

29=1×29


Here, 1 is common among 17,23 and 29.

So, HCF (17,23,29)=1


In LCM we have to multiply all number with highest power but number should not be repeated.


LCM(17,23,29)=17×23×29=11,339



3) 8,9 and 25


8= 2×2×2×1

9=3×3×1

25=5×5×1


Here, 1 is common among 8,9 and 25.

So,  HCF (8,9,25)=1


In LCM we have to multiply all number with highest power but number should not be repeated. 


LCM(8,9,25)=2×2×2×3×3×5×5=1100


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