Question

find the HCF and LCM of integers by prime factorization


1)306 and 657
2)17,23 and 29
3)8,9 and 25

Answer 1

1) 306 = 2*2*7*11 = 2*3²*17
657 =  3*3*73 = 3²*73
Lcm = product of all prime factors with highest power = 2*3²*17* 3²*73 = 201042
Hcf = product of prime factors with lowest power = 3² = 9

2) 17 = 1*17
23 = 1*23
29 = 1*29
Lcm = 1*17*1*23*1*29 = 11339
Hcf = 1

3) 8 = 2³
9 = 3²
25 = 5²
Lcm = 2³*3²*5² = 1800
Hcf = 1

Answer 2

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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