Two numbers in the ratio 15 : 11 have their HCF to be 13. What is their LCM?

Correct option is B

Given:

- The two numbers are in the ratio 15:11.
- The HCF of the two numbers is 13.

Solution:

Let the two numbers be 15x and 11x , where x is the HCF.

Since the HCF of the two numbers is given to be 13, we have x = 13 .

Thus, the two numbers are:

​$$15 \times 13 = 195 \ \text{and} \quad 11\times13 = 143.$$​​

The product of the two numbers is:

​$$195 \times 143 = 27885.$$​​

We know that the product of two numbers is equal to the product of their HCF and LCM:
HCF $$\times$$​LCM  =Product of the two numbers.

Substituting the values:

13$$\times$$​ LCM = 27885 

LCM = $$\frac{27885}{13} = 2145$$​​

The LCM of the two numbers is 2145 .