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The greatest common divisor of two integers is (x+3) and their least common multiple is x(x+3), where x is a positive integer. If one of the integers is 40, what is the smallest possible value of the other one?

Guest Jun 26, 2018
 #1
avatar+87293 
+2

  

The divisors of 40 are

1  2  4  5   8  10   20   and  40

 

But  x  is a positive integer..  and since x + 3  divides 40......the possible values for x are

 

1   2   5    7   17    37

 

So  when

 

x = 1       LCM  =  4  ( impossible....the LCM is at least 40)

x = 2       LCM  =  10

x = 5       LCM   = 40

 

So  x  =  5   and  the  other  integer  is  8

 

 

cool cool cool

CPhill  Jun 26, 2018

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