Question

Two numbers both greater than 27 having hcf 27 and lcm 162.find the sum of the numbers

Answer 1

if u meant that one is greater 27 than the other then x-y=27.... (1)
and product of two nos = hcf*lcm
means xy = 4374.... (2)

solving 1 n 2

(x-y)^2=(x+y)^2-4xy
implies (x+y)^2=(x-y)^2+4xy

(x+y)^2=27^2+4*4374

(x+y)^2=18225

x+y =135
sum of the nos 135

Answer 2

Given:

Two numbers both greater then 27,HCF=27,LCM=162

To Find:

Sum of the numbers?

Step-by-step explanation:

• Let the one number x and other number by y.

• Since we know product of number= HCF $\times$LCM

      Thus xy=4374

• NOW factors of 4374

        $2\times 3\times3\times3\times3\times3\times3\times3\\\\=27\times2\times27\times3$

• Since both number greater then 27.

• We can observe possibility of two numbers only be 54 and 71

        thus sum of number is 125

Hence, sum is 125.