+1443 sorry the problem is more sorry
How many different integers between 100 and 500 are multiples of either 6, 8,or both?
+129852 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
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
