The L.C.M of two numbers is 12 times their H.C.F. The sum of H.C.F. and L.C.M is 403. If one number is 93 , find the other.

Correct option is A

Given:

1. The LCM of two numbers is 12 times their HCF.
2. The sum of HCF and LCM is 403.
3. One of the numbers is 93.

Formula Used:

1. HCF $$\times$$ LCM = Product of the two numbers
2. The LCM is given as 12 $$\times \text{HCF}$$​ 

Solution:

1. Let the HCF of the numbers be x .
Then, LCM = 12x .

2. From the problem, $$\text{HCF} + \text{LCM}$$​ = 403 :

x + 12x = 403

13x = 403 $$\implies x = 31$$​​

So, $$\text{HCF} = 31 and \text{LCM} = 12 \times 31$$​ = 372 .

3. Using the formula $$\text{HCF} \times \text{LCM} = \text{Product of the two numbers}$$​ :

​$$31 \times 372 = 93 \times \text{Other number}$$​​


​$$11532 = 93 \times \text{Other number}$$​​


​$$\text{Other number} = \frac{11532}{93} = 124$$​​

Final Answer:

The other number is 124 .

**Option A: 124**