# Using prime factorization, find the HCF and LCM of:

Question:

Using prime factorization, find the HCF and LCM of:

(i) 8, 9, 25
(ii) 12, 15, 21
(iii) 17, 23, 29
(iv) 24, 36, 40
(v) 30, 72, 432
(vi) 21, 28, 36

Solution:

(i) 8, 9, 25

Prime factorisation:
8 = 2 × 2 × 2
9 = 3 × 3
25 = 5 × 5

HCF (8, 9, 25) = 1

LCM (8, 9, 25) = 2 × 2 × 2 × 3 × 3 × 5 × 5
= 1800

(ii) 12, 15, 21

Prime factorisation:
12 = 2 × 2 × 3
15 = 3 × 5
21 = 3 × 7

HCF (12, 15, 21) = 3

LCM (12, 15, 21) = 2 × 2 × 3 × 5 × 7
= 420

(iii) 17, 23, 29

Prime factorisation:
17 = 17
23 = 23
29 = 29

HCF (17, 23, 29) = 1

LCM (17, 23, 29) = 17 × 23 × 29
= 11339

(iv) 24, 36, 40

Prime factorisation:
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
40 = 2 × 2 × 2 × 5

HCF (24, 36, 40) = 2 × 2
= 4

LCM (24, 36, 40) = 2 × 2 × 2 × 3 × 3 × 5
= 360

(v) 30, 72, 432

Prime factorisation:
30 = 2 × 3 × 5
72 = 2 × 2 × 2 × 3 × 3
432 = 2 × 2 × 2 × 2 × 3 × 3 × 3

HCF (30, 72, 432) = 2 × 3
= 6

LCM (30, 72, 432) = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
= 2160

(vi) 21, 28, 36

Prime factorisation:
21 = 3 × 7
28 = 2 × 2 × 7
36 = 2 × 2 × 3 × 3

HCF (21, 28, 36) = 1

LCM (21, 28, 36) = 2 × 2 × 3 × 3 × 7
= 252