Question

Sum of two numbers is 135 and their H.C.F is 27. If their L.C.M is 162. Find the number.

Answer 1

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) ..