Question

For each pair of numbers, verify that their product = (HCF × LCM).
(i) 87, 145
(ii) 186, 403
(iii) 490, 1155

Answer 1

(i) 87 and 145


We have:
87 = 3 × 29
145 = 5 × 29

HCF = 29
LCM = 29 × 15 × 1 = 435

Now, HCF × LCM = 29 × 435 = 12615
Product of the two numbers = 87 × 145 = 12615

∴ HCF × LCM = Product of the two numbers
Verified.

(ii)186 and 403

186 = 2 × 3 × 31
403 = 31 × 13

HCF = 31
LCM = 31 × 13 × 6 = 2418

Now, HCF × LCM = 31 × 2418 = 74958
Product of the two numbers = 186 × 403 = 74958

∴ HCF × LCM = Product of the two numbers
Verified.

(iii) 490 and 1155

490 = 7 × 7 × 2 × 5
1155 = 5 × 7 ×3 × 11

HCF = 7 × 5 = 35
LCM = 7 × 5 ×7 × 2 × 3 × 11 = 16170

Now, HCF × LCM = 35 × 16170 = 565950
Product of the two numbers = 490 × 1155 = 565950

∴ HCF × LCM = Product of the two numbers
Verified.