Question

The HCF and LCM of two numbers are 12 and 72 respectively. if the sum of the two number is 60, what os one of the two numbers ?

Answer 1

let two numbers are x and y.
x×y= 72×6
x= 432-y. ..............(1)
x+y=60 ............(2)
solve two equations.

Answer 2

Let the two numbers be x and y.

Given that HCF * LCM of two numbers are 12 and 72.

We know that HCF * LCM = Product of two numbers

12 * 72 = x * y

864 = xy   ----------------- (1)


Given that sum of two numbers = 60.

x + y = 60.

y = 60 - x    ---------------- (2)


Substitute (2) in (1), we get

xy = 864

x * (60 - x) = 864

60x - x^2 = 864

-x^2 + 60x - 864 = 0

-1(x^2 - 60x + 864) = 0

x^2 - 60x + 864 = 0

x^2 - 36x - 24x + 864 = 0

x(x - 36) - 24(x - 36) = 0

(x - 36) = 0 (or) x - 24 = 0

x = 36 and 24.


Therefore the 2 numbers are 36 and 24.