#2**+1 **

The number of multiples of 19 < 775 = 775 / 19 = 40

And their sum = 19 (40)(41)/2 = 15580

The number of multiples of 5 < 775 = 770 / 5 = 154

And their sum = 5 (154)(155) / 2 = 59675

However....we must subtract out the sum of all numbers divisible by both 5 and 19.......this will equal all the multiples of 19 * 5 = 95.......so 775/95 = 8

So...the sum of these = 95 (8) (9)/2 = 3420

So...the total sum of all multiples of 5 or 16 less than 775 = [ 15580 + 59675 - 3420 ] = 71835

CPhill
May 25, 2017

#1**0 **

Find the sum of the multiples of 19 or 5 under 775.

Well, the easiest way to do it is as follows:

775 / 19 =40.7894....... Just drop the fraction and keep 40. That means there are 40 multiples of 19 up to 775.

Now, you can use an Arithmetic Progression to add them up:

Sum =n/2[2a + (n - 1)d] =40/2[2*19 + (40 - 1)*19] =20[38 + 741] =15,580 - which is the total of all multiples of 19 up to 775.

Now, do exactly the same thing with 5 =775 / 5 =155. This is how many multiples of 5 you have up to 775.

Use the same formula as above to add them all up. If you do it right, you should get a total of =60,450. Now, try to see if you get the same number. Good luck.

Guest May 25, 2017

edited by
Guest
May 25, 2017

#2**+1 **

Best Answer

The number of multiples of 19 < 775 = 775 / 19 = 40

And their sum = 19 (40)(41)/2 = 15580

The number of multiples of 5 < 775 = 770 / 5 = 154

And their sum = 5 (154)(155) / 2 = 59675

However....we must subtract out the sum of all numbers divisible by both 5 and 19.......this will equal all the multiples of 19 * 5 = 95.......so 775/95 = 8

So...the sum of these = 95 (8) (9)/2 = 3420

So...the total sum of all multiples of 5 or 16 less than 775 = [ 15580 + 59675 - 3420 ] = 71835

CPhill
May 25, 2017