Question

The product of LCM and HCF of any two numbers is equal to the product of the numbers.

• A. True
• B. False

Answer 1

The correct option is A

True

The product of LCM and HCF of any two numbers is equal to the product of the numbers.

For example, take two numbers 12 and 18.
First, we need to find the highest common factor (HCF) of 12 and 18.

12 = 2 $\times$ 2 $\times$ 3

18 = 2 $\times$ 3 $\times$ 3

$\therefore$ HCF of 12 and 18 = 2 $\times$ 3 = 6
Lowest common multiple (LCM) of 12 and 18 = 2 x 2 x 3 x 3 = 36.

HCF × LCM = 6 × 36 = 216

Also 12 × 18 = 216

Therefore, product of HCF and LCM of 12 and 18 = product of 12 and 18.