999/3there are 333 multiples of 3
The first multiple of 3 is 3; the last multiple of 3 below 1000 is 999. (This can be determined by dividing 1000 by 3, ignoring the remainder, and then multiplying that number by 3 to determine the largest multiple of 3 less than 1000.) Since 999 is 3 times 333, there are 333 multiples of 3 that are less than 1000. So, consider them by pairs: 1st and 333rd = 3 + 999 = 1002 2nd and 332nd = (2 x 3) + (332 x 3) = 6 + 996 = 1002 3rd and 331st = (3 x 3) + (331 x 3) = 9 + 993 = 1002 up to 166th and 168th = (166 x 3) + (168 x 3) = 498 + 504 = 1002 167th = 501 (which is half of 1002) In other words, since 333 is not an even number, there are (333 - 1)/2 = 166 pairs, plus that extra half of a pair. The sum of all the multiples of 3 less than 1000 is 166.5 x 1002 = 166,833. The same can be done for the multiples of 5. The first multiple of 5 is 5; the last multiple of 5 below 1000 is 995. (This can be determined by dividing 1000 by 5, subtracting 1 since it divided evenly and you need the largest multiple less than 1000, and then multiplying that number by 5 to determine the largest multiple of 5 less than 1000.) Since 995 is 5 times 199, there are 199 multiples of 5 that are less than 1000. So, consider these by pairs as well.e are 1st and 199 = 5 + 995 = 1000 2nd and 198 = 10 + 990 = 1000 up to 100th = 500 (which is half of 1000) In other words, since 199 is not an even number, there are (199 - 1)/2 = 99 pairs, plus that extra half of a pair. So, the sum of all the multiples of 5 less than 1000 is 99.5 x 1000 = 99,500. If the desired answer is the sum of all numbers less than 1000 that are either multiples of 3 or 5, then the numbers that are multiples of both 3 and 5 have been included twice - once as multiples of 3 and again as multiples of 5. So, since all numbers that are both multiples of 3 and multiples of 5 are multiples of 15, determine the sum of all the multiples of 15 and subtract it from the sum of the multiples of 3 and the multiples of 5. We can repeat the same procedure again. The first multiple of 15 is 15; the last multiple of 15 less than 1000 is 990. Since 990 is 15 x 66, there are 66 multiples of 15 less than 1000. 1st and 66th = 15 + 990 = 1005 2nd and 65th = 30 + 975 = 1005 and so on Since 66 is an even number, there are 66/2 = 33 pairs. So the sum of all the multiples of 15 less than 1000 is 33 x 1005 = 33,165. The sum of all the multiples of 3 and all the multiples of 5, but not counting them twice, is 166,833 + 99,500 - 33,165 = 233,168.
297
The multiples of 4 are numbers that can be divided evenly by 4. To find all the multiples of 4 from 1 to 1000, we can start by finding the first multiple of 4, which is 4. Then we can continue adding 4 to find the rest of the multiples. The multiples of 4 from 1 to 1000 are: 4, 8, 12, 16, ... , 996, 1000.
The first three multiples of 3 are 3, 6, 9 The first three multiples of 9 are 9, 18, 27 As the lowest common multiples of 3 and 9 is 9, the common multiples of 3 and 9 are the multiples of 9, thus: The first three common multiples of 3 and 9 are 9, 18, 27
999/3there are 333 multiples of 3
Not counting zero, the first five multiples are 200, 400, 600, 800, and 1000. (200 times 1, 2, 3, 4, and 5)
333
The first 50 multiples of 6 are the first fifty even multiples of 3.
The first multiple of 3 is 3; the last multiple of 3 below 1000 is 999. (This can be determined by dividing 1000 by 3, ignoring the remainder, and then multiplying that number by 3 to determine the largest multiple of 3 less than 1000.) Since 999 is 3 times 333, there are 333 multiples of 3 that are less than 1000. So, consider them by pairs: 1st and 333rd = 3 + 999 = 1002 2nd and 332nd = (2 x 3) + (332 x 3) = 6 + 996 = 1002 3rd and 331st = (3 x 3) + (331 x 3) = 9 + 993 = 1002 up to 166th and 168th = (166 x 3) + (168 x 3) = 498 + 504 = 1002 167th = 501 (which is half of 1002) In other words, since 333 is not an even number, there are (333 - 1)/2 = 166 pairs, plus that extra half of a pair. The sum of all the multiples of 3 less than 1000 is 166.5 x 1002 = 166,833. The same can be done for the multiples of 5. The first multiple of 5 is 5; the last multiple of 5 below 1000 is 995. (This can be determined by dividing 1000 by 5, subtracting 1 since it divided evenly and you need the largest multiple less than 1000, and then multiplying that number by 5 to determine the largest multiple of 5 less than 1000.) Since 995 is 5 times 199, there are 199 multiples of 5 that are less than 1000. So, consider these by pairs as well.e are 1st and 199 = 5 + 995 = 1000 2nd and 198 = 10 + 990 = 1000 up to 100th = 500 (which is half of 1000) In other words, since 199 is not an even number, there are (199 - 1)/2 = 99 pairs, plus that extra half of a pair. So, the sum of all the multiples of 5 less than 1000 is 99.5 x 1000 = 99,500. If the desired answer is the sum of all numbers less than 1000 that are either multiples of 3 or 5, then the numbers that are multiples of both 3 and 5 have been included twice - once as multiples of 3 and again as multiples of 5. So, since all numbers that are both multiples of 3 and multiples of 5 are multiples of 15, determine the sum of all the multiples of 15 and subtract it from the sum of the multiples of 3 and the multiples of 5. We can repeat the same procedure again. The first multiple of 15 is 15; the last multiple of 15 less than 1000 is 990. Since 990 is 15 x 66, there are 66 multiples of 15 less than 1000. 1st and 66th = 15 + 990 = 1005 2nd and 65th = 30 + 975 = 1005 and so on Since 66 is an even number, there are 66/2 = 33 pairs. So the sum of all the multiples of 15 less than 1000 is 33 x 1005 = 33,165. The sum of all the multiples of 3 and all the multiples of 5, but not counting them twice, is 166,833 + 99,500 - 33,165 = 233,168.
The 3 first multiples of 75 are: 1, 3, and 5.
297
The sum of the first 10 multiples of 3 is 165.
The first 3 multiples of 17 are: 17, 34, 51
All multiples of 3 have digits that add up to a multiple of 3. There are 333 multiples of 3 between 1 and 1000.
The first three multiples of 3 are 3, 6, 9 The first three multiples of 9 are 9, 18, 27 As the lowest common multiples of 3 and 9 is 9, the common multiples of 3 and 9 are the multiples of 9, thus: The first three common multiples of 3 and 9 are 9, 18, 27
All multiples of 12, such as 120, 600, 660.