28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, . . .
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To find the positive integers less than 2009 that are divisible by 28 but not by 12, we need to find the multiples of 28 that are not multiples of 12. The least common multiple of 28 and 12 is 84, so we need to find multiples of 28 that are not multiples of 84. Since 28 = 2^2 * 7 and 84 = 2^2 * 3 * 7, the multiples of 28 that are not multiples of 84 are those that have an odd power of 2. The highest multiple of 28 less than 2009 that satisfies this condition is 1976. Therefore, there are 1976 / 28 = 71 positive integers less than 2009 that are divisible by 28 but not by 12.
21 and 28
LCM of 4,7,14 is 28 So question boils down to multiples of 28 between 61 and 107 Multiples of 28 are 28, 58, 84, 112, 140, ... So the answer is just 84.
28, 56, 84, 112, 140, 168, 196, 224.