Question

2. For the following pairs of numbers, show that the product of their HCF and LCM
equals their product:
(i) 21, 28
(ii) 144, 196 (iii) 36, 76 (iv) 120, 350
​

Answer 1

Answer:

lcm 21=3×7

lcm 28=2×2×7

hcf 21,28=7

the equal product is 42 and 14 = 7

Answer 2

Answer:

(i) 21, 28

Factors of 21 = 3 × 7

Factors of 28 = 2 × 7 × 2

LCM(21, 28) = 3 × 7 × 2² = 21 × 4 = 84

HCF(21, 28) = 7

HCF × LCM = 21 × 28

7 × 84 = 588

588 = 588

(ii) 144, 196

Factors of 144 = 2 × 2 × 3 × 2 × 2 × 3

Factors of 196 = 7 × 2 × 2 × 7

LCM(144, 196) = 7² × 3² × 2³ × 2 = 49 × 9 × 8 ×2 = 7056

HCF(144, 196) = 2 × 2 = 4

7056 × 4 = 144 × 196

28224 = 28224

(iii) 36, 76

Factors of 36 = 2 × 3 × 3 × 2

Factors of 76 = 2 × 2 × 19

LCM(36, 76) = 2² × 3² × 19 = 684

HCF(36, 76) = 2² = 4

684 × 4 = 36 × 76

2736 = 2736

(iv) 120, 350

Factors of 120 = 2 × 2 × 3 × 2 × 5

Factors of 350 = 2 × 5 × 5 × 7

LCM(120, 350) = 2³ × 5² × 7 × 3 = 4200

HCF(120, 350) = 2 × 5 = 10

10 × 4200 = 120 × 350

42000 =  42000

Hope this helps you!!!