FINDING HCF AND LCM USING LADDER METHOD

HCF (Highest common factor) :

A common factor is a number that is a factor of two or more other numbers.

The highest common factor (HCF) is the largest factor that is common to two or more numbers.

LCM (Least common Multiple) : 

The least common multiple of two or more numbers is the smallest non zero which is a multiple of all numbers.

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

Problem 1 :

9, 12

Solution :

HCF of (9, 12) = 3

LCM of (9, 12) = 4 x 32 ==> 36 

Problem 2 :

8, 16

Solution :

8, 16

HCF of (8, 16) = 23 ==> 8

LCM of (8, 16) = 24 ==> 16

Problem 3 :

18, 42

Solution :

18, 42

HCF of (18, 42) = 3 × 2 ==> 6

LCM of (18, 42) = 32 × 2 x 7 ==> 126

Problem 4 :     

14, 42

Solution :

14, 42

HCF of (14, 42) = 2 × 7 ==> 14

LCM of (14, 42) = 2 × 3 x 7 ==> 42

Problem 5 :

18, 30

Solution :

18, 30

HCF of (18, 30) =  3 × 2 ==> 6

LCM of (18, 30) =  32 × 2 x 5 ==> 90

Problem 6 :

24, 32

Solution :

24, 32

HCF of (24, 32) = 23 ==> 8

LCM of (24, 32) = 25 x 3 ==> 96

Problem 7 :

12, 36

Solution :

12, 36

HCF of (12, 36) = 3 × 2==> 12

LCM of (12, 36) = 32 × 2 ==> 36

Problem 8 :

15, 33

Solution :

15, 33

HCF of (15, 33) = 3

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

Problem 9 :

72, 96

Solution :

72, 96 

HCF of (72, 96) = 3 × 2==> 24

LCM of (72, 96) = 32 × 2==> 288

Problem 10 :

108, 144

Solution :

108, 144

HCF of (108, 144) = 22 x 3==> 36

LCM of (108, 144) = 24 x 3==>  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

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