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Q. The number of natural numbers less than 400 that are not divisible by 17 or 23 is

Sequences and Series

Solution:

divisible by 17 and less than $400$
$17, 34, 51, ........ 391 (23)$
divisible by 23 but less than $400$
$23, 46, 69,.........391 (17)$
divisible by both
$391 (1)$
divisible by 17 or $23 = 23 + 17 - 1 = 39$
not divisible by 17 or 23 and $< 400$
$= 399 - 39 = 360 $