+0  
 
0
277
5
avatar+435 

How many multiples of 8 are between 100 and 500?

SmartMathMan  Jan 9, 2018
 #1
avatar+87294 
+1

[ 500  -  100 ]    /  8    -    1   =

 

400 /  8    -   1 =

 

50  -  1   =

 

49 multiples   "between"

 

 

cool cool cool

CPhill  Jan 9, 2018
 #2
avatar+435 
0

sorry the problem is more sorry

 

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

SmartMathMan  Jan 9, 2018
 #3
avatar+87294 
+1

Multiples  of  8  =  

 

[500 - 100 ] /  8  -   1  =  50  -  1   =  49  between

 

Multiples of 6  =

 

[ 500 - 100 ] / 6  -  1   =  66 between

 

The LCD  for 6, 8  is 24....we must subtract the multiples of 24 between 100  and 500 from the above total

 

[ 500 - 100] / 24  =  16 between 

 

So.....the total multiples of 6, 8 (or both) between 100 and 500  =

 

49 + 66  -  16   =

 

99

 

 

cool cool cool

CPhill  Jan 9, 2018
 #4
avatar
+2

These are simply the number of terms in Arithmetic Series:

Number of terms =[ Last term - First term] / Common diffrence + 1

N =[496 - 104] / 8 + 1

N=[ 392] / 8 + 1

N= 49 + 1

N = 50 - multiples of 8 between 100 and 500

 

N =[ 498 - 102] / 6 + 1

N =[ 396 ] / 6 + 1

N= 66 + 1

N = 67 - multiples of 6 between 100 and 500

Total = 50 + 67 =117 - multiples of 6 and 8 between 100 and 500.

However, 6 and 8 have an LCM of 24.Therefore, multiples of 24 between 100 and 500 are

N = 16 - multiples of 24 between 100 and 500 which have been counted TWICE!. So the number of integers that are multiples of 6 and 8, or both, between 100 and 500 is:

117 - 16 = 101 Integers

Guest Jan 9, 2018
 #5
avatar+26745 
0

I'm in agreement with Guest#4 on this one!

Alan  Jan 9, 2018

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