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How many different integers between 100 and 500 are multiples of either 6, 8, or both?

 Feb 10, 2022
 #1
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Multiples of 6   =  102 , 108 ........498

So.....the number of multiples divisble by 6 =    [498 - 102 ]  /  6  + 1  =   66 + 1  =  67

 

Multiples of  8  =   104, 112 .......496

So  ...      [ 496 - 104 ] / 8  +   1 =  49 + 1   = 50

 

We  need  to add  all those divisible  by 6,8...i.e.,   the LCM of 6,8  =  24

 

So....Multiples of 24   =   120, 144 ......480

So....  [ 480  - 120 ]  / 24   +  1   =  15 + 1  = 16

 

So

Divisible by 6   +  Divisible by 8  +  Divisible by 24 =

     67               +          50           +        16    =                  133

 

 

cool cool cool

 Feb 10, 2022
 #2
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Welcome back CPhill.

 

Shouldn't multiples of 24 be subtracted from multiples of 6 + multiples of 8, since they are already included in the totals of the two?

 

67 + 50 - 16 ==101 such multiples.

 Feb 11, 2022

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