# Q.11. Three numbers are such that the first is $\frac{1}{3}$ of the second and the third is $\frac{2}{5}$ of the sum of the first and second. If their LCM is 120, then find the third number.

Dear Student,

Please find below the solution to the asked query:

Let , first number  =  , So  from given condition we get :

Second number  = $\frac{x}{3}$

And from second condition we get :

Third number =

Also given : L.C.M. of these three numbers  = 120

And we know L.C.M. of fractions  =

So,

L.C.M. ( x , x and 8 x ) =  8 x

And

H.C.F ( 1 , 3 and 15 ) =  1

So,

8x  = 120 ,

x  = 15

Then,

First number = 15  , Second number  = $\frac{15}{3}$ = 5  and Third number  = = 8                                   ( Ans )
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• 1
i think third term is 8
• 1
But how. Can u give me with solution
• 0
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