The sum of two numbers is 135 and their HCF is 27 if their LCM is 162 then find the numbers

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let the two no. be x and y respectively.

then, 

        x+y=135

 27 is their HCF

so each no. must be divisible by 27.

so let x=27a and y= 27b ;

now, 27a + 27b=135

           a + b =135/27

            a + b= 5

           so possible values for (a,b) are (1,4), (2,3)  order can be reverse it (1,4) gives (27,108)  is not possible its LCM is 108 (2,3) gives (54,81) is possible answer its LCM is 162  no. could be (54,81) and s(81,54)  ..