# What are the multiples of 3

Assuming you mean that you want the number of multiples of each, then for 1-100: number of multiples of 2 = 50 number of multiples of 3 = 33 number of multiples of 4 = 25 number of multiples of 6 = 16 number of multiples of 8 = 12 number of multiples of 9 = 11 Assuming you mean that you want the numbers that are multiples of 2, 3, 4, 6, 8 or 9, then some numbers may be multiples of more than one (for example 12 is a multiple of 2, 3, 4 and 6) and so a straight addition of the number of multiples of each cannot be done: Consider 2, 4 and 8 Every multiple of 4 or 8 is also a multiple of 2, so all the multiples of 4 and 8 are counted by the multiples of 2. Consider 3 and 9 Every multiple of 9 is also a multiple of 3, so all the multiples of 9 are counted by the multiple of 3 Consider 2, 3 and 6. Every multiple of 6 is an even multiple of 3, so are counted in both the multiples of 2 and 3. So the total number of multiples of 2, 3, 4, 6, 8 or 9 is the number of multiples of 2 plus the number of multiples of 3 minus the number of multiples of 6: For 1 to 100, Number of multiples of 2 = 50 Number of multiples of 3 = 33 Number of multiples of 6 = 16 So number of multiples of 2, 3, 4, 6, 8 or 9 in 1-100 is 50+33-16 = 67. Assuming you mean that they are multiples of all of 2, 3, 4, 6, 8 and 9, then they must be multiples of the lowest common multiple of 2, 3, 4, 6 ,8, 9 2 = 21, 3 = 31, 4 = 22, 6 = 2131, 8 = 23, 9 = 32 LCM = highest power of the primes used = 2332 = 72 Thus all numbers that are multiples of 2, 3, 4, 6, 8 and 9 are multiples of 72, which means between 1 and 100 only 1 number is a multiple of all of them, namely 72

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