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X is a multiple of 15 and a multiple of 35. X is less than 600. How many possible values of X are there?

Correct Answer:

**E**Be careful not to double count

- If X is a multiple of 15, then it must be divisible by 5 and 3. If X is multiple of 35, then it must be divisible by 7 and 5.Therefore X must be divisible by 3, 5, and 7. 3*5*7 = 105. Therefore 105 is the smallest possible X.
- Any other possible X must be a multiple of 105 since X must have 3, 5, and 7 as factors. Multiples of 105 that are less than 600 are 105, 210, 315, 420, and 525. There are 5 possibilities.