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There are 1000 integers from 1 to 1000. Only the multiples of 30 of these integers are divisible by 30, such as 30, 60, 90, 120, 150, 180, 210, 240, ..., 990.

Since the LCM of 16 and 30 is 240, then only 7 integers from 1 to 1,000 are divisible by 30 but not by 16, which are 30, 60, 90, 120, 150, 180, and 210.

(Prime factorization:

30 = 2 x 3 x 5

16 = 24

The LCM of 30 and 16 is 24 x 3 x 5 = 240.)

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Md shimul Parvez

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Q: How many integers from 1 to 1000 are divisible by 30 but not by 16?
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