The L.C.M of two numbers is 156 and their H.C.F is 2. If the sum of the numbers is 38, then their di

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13 Mar 2018 LCM HCF

The L.C.M of two numbers is 156 and their H.C.F is 2. If the sum of the numbers is 38, then their difference is

OPtion

1) 10
2) 8
3) 9
4) 12
5) 11
6) 14
7) 13
8) 15
9) 16
10) None of these

Solution

Let the numbers be x and (38-x).
Then,
x*(38-x) = 156*2
=> x^2 - 38x + 26*12 = 0
=> x^2 - 26x - 12x + 26*12 = 0
=> x (x-26) -12(x-26) = 0
=> (x-12)(x-26) = 0
The numbers are 12 and 26
Required difference = (26-12) = 14

Correct Option: 6 Best Solution (0)