Question

if the difference between the two specific numbers is 12,the LCM of two numbers is 63 and HCF of two numbers is 3,then sum of the two numbers is ?​

Answer 1

Answer:

Difference between 2 numbers = 12

LCM of the two numbers = 63

HCF of the two numbers = 3

Let the number be a and b

a - b = 12

a = 12 + b

We know that

LCM * HCF = (Product of two numbers) a*b

63 * 3 = ab

189 = ab

189 = (12 + b)b

189 = 12b + b^2

b^{2} + 12b - 189 = 0

Finding the factors

b^{2} + 9b - 21b-189= 0

b(b + 9) - 21(b + 9) = 0

(b - 21), (b + 9) = 0

Either

b = 0 + 21

= 21

OR,

b = 0 - 9

= -9

Since number can't be negative.

So

b = 21

a = 21 + 12 = 33

So sum of the two numbers is =33+21=54

Answer 2

Answer:

Given,

difference of two numbers = 12

LCM of two numbers = 63

HCF of two numbers = 3

to find = sum of two numbers

Explanation:

Let the two numbers be x and y

x-y = 12

x = 12 + y --------------------(1)

LCM × HCF = Product of two numbers

63 × 3 = x × y

189 = xy. ------------------(2)

put the value of x from eqn(1) in eqn (2),

189 = (12+y)y

$189 = 12y + {y}^{2} \\ {y}^{2} + 12y - 189 = 0$

by factorisation,

y = 21 or y = -9

by ignoring negative number,

we get the value of y = 21

x = 12+21= 33

sum of the number = 33 + 21 = 54