The ratio of two numbers is 3 : 4 and their HCF is 4. Their LCM is:

Correct option is A

Given:

The ratio of the two numbers is 3 : 4.

The HCF of the two numbers is 4.

Formula Used:

​$$\text{LCM} \times \text{HCF} = \text{Product of the numbers}$$​​

Solution:

Let the two numbers be 3x and 4x, where x is a constant.

Since their HCF is given as 4, the constant x must be 4.

Thus, the two numbers are:

​$$3x = 3 \times 4 = 12\\4x = 4 \times 4 = 16$$​​

The product of the two numbers:

​$$\text{Product of the numbers} = 12 \times 16 = 192$$​​

​$$\text{LCM} = \frac{\text{Product of the numbers}}{\text{HCF}} = \frac{192}{4} = 48$$​​

Thus, the LCM of the two numbers is 48.