Question

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
(iv) 40,36 and 126 (v) 84, 90 and 120 (vi) 24, 15 and 36

Answer 1

TO FIND: LCM and HCF of following pairs of integers

(i) 15, 12 and 21

Let us first find the factors of 15, 12 and 21

12 = 2 x 2 x 3

15 = 3 x 5

21 = 3 x 7

L.C.M of 12, 15 and 21 = 2 x 2 x 3 x 5 x 7

L.C.M of 12, 15 and 21 = 420

H.C.F of 12, 15 and 21 = 3

(ii) 17, 23 and 29

Let us first find the factors of 17, 23 and 29

17 = 1 x 17

23 = 1 x 23

29 = 1 x 29

L.C.M of 17, 23 and 29 = 1 x 17 x 23 x 29

L.C.M of 17, 23 and 29 = 11339

H.C.F of 17, 23 and 29 = 1

(iii) 8, 9 and 25

Let us first find the factors of 8, 9 and 25

8 = 2 x 2 x2

9 = 3 x 3

25 = 5 x 5

L.C.M of 8, 9 and 25 =2³ x 3² x 5²

L.C.M of 8, 9 and 25 = 1800

H.C.F of 8, 9 and 25 = 1

(iv) 40, 36 and 126

Let us first find the factors of 40, 36 and 126

40 = 2³ x 5

36 = 2³ x 3²

126 = 2 x 3 x 3 x 7

L.C.M of 40, 36 and 126 = 2³ x 3² x 5 x 7

L.C.M of 40, 36 and 126 = 2520

H.C.F of 40, 36 and 126 = 2

(v) 84, 90 and 120

Let us first find the factors of 84, 90 and 120

84 = 2 x 2 x 3 x 7

90 = 2 x 3 x 3 x 5

120 = 2 x 2 x 2 x 3 x 5

L.C.M of 84, 90 and 120 = 2³ x 3² x 5 x 7

L.C.M of 84, 90 and 120 = 2520

H.C.F of 84, 90 and 120 = 6

(vi) 24, 15 and 36

Let us first find the factors of 24, 15 and 36

24 = 2³ x 3

15 = 3 x 5

36 = 2 x 2 x 3 x 3

LCM of 24, 15 and 36 = 2 x 2 x 2 x 3 x 3 x 5

LCM of 24, 15 and 36 = 360

HCF of 24, 15 and 36 = 3