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Find the sum of the multiples of 7 or 19 under 922

 Jul 14, 2014

Best Answer 

 #1
avatar+33661 
+5

There are just over 131 7's in 922 (922/7 = 131.7...), so the sum of all the multiples is given by 7*(1+2+3+...+131).

This is 7*131*132/2 = 60522

There are just over 48 19's in 922 (922/19 = 48.5...), so the sum of all these multiples is 19*(1+2+...+48)

This is  19*48*49/2 = 22344

If you meant the sum of both, then 

(1) total is 60522+22344 = 82866 unless you don't want common multiples counted twice.

(2) Since there are 6 common multiples the sum of these is 7*19*(1+2+...+6) = 7*19*6*7/2 = 2793. This is counted twice, so we subtract this from 82866 to get 80073.

 Jul 14, 2014
 #1
avatar+33661 
+5
Best Answer

There are just over 131 7's in 922 (922/7 = 131.7...), so the sum of all the multiples is given by 7*(1+2+3+...+131).

This is 7*131*132/2 = 60522

There are just over 48 19's in 922 (922/19 = 48.5...), so the sum of all these multiples is 19*(1+2+...+48)

This is  19*48*49/2 = 22344

If you meant the sum of both, then 

(1) total is 60522+22344 = 82866 unless you don't want common multiples counted twice.

(2) Since there are 6 common multiples the sum of these is 7*19*(1+2+...+6) = 7*19*6*7/2 = 2793. This is counted twice, so we subtract this from 82866 to get 80073.

Alan Jul 14, 2014

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