# What will be the Sum of the Number? If

The HCF and LCM of two numbers are 12 and 2448 respectively. If the difference of the numbers is 60, then the sum of the number is

- 248
- 204
- 348
- 284

Given data: LCM = 2448 , HCF = 12 and

difference of numbers = 60

We know that,

**LCM * HCF of two numbers = Multiplication of both numbers**

Let a and b are two numbers, Then

a * b = LCF * HCF

a * b = 12 * 2448 = 29376 — eqn. (1)

a – b = 60 ; given in question

as, (a – b)^{2} = a^{2} + b^{2} – 2ab and

as (a + b)^{2} = a^{2} + b^{2} + 2ab

(a + b)^{2} = (a – b)^{2} + 4ab

(a + b)^{2} = 60*60 + 4*29376

(a + b)^{2} = 121104

(a + b) = sqrt(121104)

(a + b) = 348

**Answer: Sum of two numbers = 348**