Question

Find the LCM and HCF of the following integers by applying the prime factorization method.
(i) 12, 15 and 21
(ii) 17, 23 and 29
(iii) 8, 9 and 25
(iv) 40, 36 and 126
(v) 84, 90 and 12
(vi) 24, 15 and 36

Answer 1

1) lcm=420 and hcf=3

Answer 2

(i) 12, 15 and 21

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 15 are: 1, 3, 5, 15

The factors of 21 are: 1, 3, 7, 21

LCM = 420

HCF = 3

(ii) 17, 23 and 29

The factors of 17 are: 1, 17

The factors of 23 are: 1, 23

The factors of 29 are: 1, 29

LCM = 11339

HCF = 1

(iii) 8, 9 and 25

The factors of 8 are: 1, 2, 4, 8

The factors of 9 are: 1, 3, 9

The factors of 25 are: 1, 5, 25

LCM = 1800

HCF = 1

(iv) 40, 36 and 126

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

The factors of 126 are: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

LCM = 2520

HCF = 2

(v) 84, 90 and 12

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

LCM = 1260

HCF = 6

(vi) 24, 15 and 36

The factors of 15 are: 1, 3, 5, 15

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

LCM = 360

HCF = 3