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

  1. 248
  2. 204
  3. 348
  4. 284
Monis Rasool Professor Asked on 14th September 2015 in Maths.
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1 Answer(s)

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 = a2 + b2 – 2ab and

as (a + b)2 = a2 + b2 + 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

Pushpendra Pal Dean Answered on 14th September 2015.
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