Find the sum of first 20 positive integers which are divisible by 5 and 6
Answers
Assuming that we are only adding whole numbers that are evenly divisible by 5 or 7, (or both) we consider the following multiples of 5 and 7:
5,10,15,20,25,30,35,40,45,50,55,60,
The sum of the preceding integers may be written as : 5*(1+2+3+4+5+6+7+8+9+10+11+12) = 5*78=390
7,14,21,28,35,42,49,56,63,
Again, the sum of the preceding values can be written similarly as: 7*(1+2+3+4+5+6+7+8+9) = 7*45=315. Of course, since we’ve included the integer 35 twice (it’s the LCM of 5 and 7), it must be subtracted from the 2nd sum, so that 315 - 35 = 280
Now we have the 1st 12 multiples of 5 (including 35) and the 1st 8 multiples of 7 (excluding 35) with no other common multiples. Adding 280 and 390 gives us 670 as the total sum.
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Answer:
6300 is the answer for the given problem
