The ratio of two numbers is 3 : 7 and their HCF is 3. Their LCM is:

Correct option is D

Given:

The ratio of two numbers is 3 : 7.

Their HCF is 3.

We need to find their LCM.

Formula Used:

HCF × LCM = Product of the two numbers

Solution:

Let the two numbers be 3x and 7x, where x is a constant multiplier.

Their HCF is 3, so:

HCF(3x,7x) = 3

Since HCF(3x, 7x) = x , we have x = 3.

The two numbers are:

3x = $$3 \times 3 = 9 \quad \text{and} \quad 7x = 7 \times 3 = 21$$​

Now, calculate the LCM:

LCM(9,21) = $$\frac{9 \times 21}{\text{HCF}(9, 21)}$$​

LCM(9,21) =$$\frac{9 \times 21}{3} = \frac{189}{3} = 63$$​

Thus, the LCM of the two numbers is 63.