Prime Factorization Method to Find HCF and LCM

Find the HCF of LCM of following numbers using prime factorization method :

Problem 1 :

9, 12

Solution :

9 = 3 × 3 ==> 3²

12 = 2 x 2 × 3 ==> 2² x 3

HCF of (9, 12) = 3

LCM of (9, 12) = 2² x 3² ==> 36 

Problem 2 :

8, 16

Solution :

8, 16

8 = 2 × 2 x 2 ==> 2³

16 = 2 × 2 × 2 x 2 ==> 2⁴

HCF of (8, 16) = 2³ ==> 8

LCM of (8, 16) = 2⁴ ==> 16

Problem 3 :

18, 42

Solution :

18, 42

18 = 3 × 3 × 2 ==> 3² x 2

42 =  3 × 2 × 7

HCF of (18, 42) = 3 × 2 ==> 6

LCM of (18, 42) = 3² × 2 x 7 ==> 126

Problem 4 :     

14, 42

Solution :

14, 42

14 = 2 × 7

42 = 2 × 3 × 7

HCF of (14, 42) = 2 × 7 ==> 14

LCM of (14, 42) = 2 × 3 x 7 ==> 42

Problem 5 :

18, 30

Solution :

18, 30

18 = 3 × 3 × 2 ==> 3² x 2

 30 = 3 × 2 × 5

HCF of (18, 30) =  3 × 2 ==> 6

LCM of (18, 30) =  3² × 2 x 5 ==> 90

Problem 6 :

24, 32

Solution :

24, 32

24 =  2 × 2 × 2 × 3 ==> 2³ x 3

32 =  2 × 2 × 2 × 2 × 2 ==> 2⁵

HCF of (24, 32) = 2³ ==> 8

LCM of (24, 32) = 2⁵ x 3 ==> 96

Problem 7 :

12, 36

Solution :

12, 36

12 = 3 × 2 × 2 ==> 2² x 3

36 = 3 × 3 × 2 × 2 ==> 3² x 2² 

HCF of (12, 36) = 3 × 2² ==> 12

LCM of (12, 36) = 3² × 2²  ==> 36

Problem 8 :

15, 33

Solution :

15, 33

15 = 3 × 5

33 = 3 × 11

HCF of (15, 33) = 3

LCM of (15, 33) = 3 x 11 x 5 ==> 165

Problem 9 :

72, 96

Solution :

72, 96 

72 = 3 × 3 × 2 × 2 ==> 3² x 2²

96 = 3 × 2 × 2 × 2 × 2 × 2 ==> 3 x 2⁵

HCF of (72, 96) = 3 × 2² ==> 12

LCM of (72, 96) = 3² × 2⁵ ==> 288

Problem 10 :

108, 144

Solution :

108, 144

108 = 2 x 2 x 3 x 3 x 3

= 2² x 3³

144 = 2 x 2 x 2 x 2 x 3 x 3

= 2⁴ x 3²

HCF of (108, 144) = 2² x 3² ==> 36

LCM of (108, 144) = 2⁴ x 3³ ==>  432

Problem 11 :

78, 130

Solution :

78, 130

78 = 2 × 3 x 13

130 = 2 × 5 x 13

HCF of (78, 130) ==> 26

LCM of (78, 130) = 2 x 5 x 3 x13 ==> 390