3. 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
Answers
Answer:
LCM : 1. 3
2. 1
3. 1
HCF : 1. 420
2. 11339
3. 1800
Step-by-step explanation:
In number 1 , 3 is the common factor. In number 2 & 3 , there is no common factor except 1.
In number 1 , 3 is the common factor whereas 4,5 & 7 are the other factors. So multiply the 3 with 4,5 &7 .
In number 2 , all are prime numbers . So multiply 17 ,23 & 29.
In number 3, 25 is the prime number but there is no common factor between 8 &9. So multiply 8 ,9 and 25.
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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