The HCF of two numbers is 11 and other two factors of their LCM are 13 and 17. The smaller of the two numbers is,

Correct option is C

Concept/Formula Used:

For two numbers, the relationship between their HCF and LCM is given by:

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

Let the two numbers be a and b , and their HCF be h . Then:

$$a = h \times m \quad \text{and} \quad b = h \times n$$​

where m and n are co-prime factors of the LCM.

The LCM of a and b is given by:

LCM = $$h \times m \times n$$​

Step 1: Given Information:

- HCF ( h ) = 11
- The other two factors of the LCM are 13 and 17.
Thus:

LCM = $$11 \times 13 \times 17 = 2431$$​

Step 2: Assume the Smaller Number:

Let the smaller number be:

$$a = h \times m = 11 \times 13 = 143$$​

Step 3: Verify the Larger Number:

The larger number will be:

$$b = h \times n = 11 \times 17 = 187$$​

Step 4: Verify the LCM:

The LCM of a and b is:

$$\text{LCM} = h \times m \times n = 11 \times 13 \times 17 = 2431$$​

This satisfies the given condition.

Correct Answer:

(C) 143