Find the number of positive integers less than 601 that are not divisible by 4 or 5 or 6

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The number of positive integers less than 601 that are divisible by 4

$\lbrack\dfrac{600}{4}\rbrack=150$

The number of positive integers less than 601 that are divisible by 6

$\lbrack\dfrac{600}{6}\rbrack=100$

The number of positive integers less than 601 that are divisible by 5

$\lbrack\dfrac{600}{5}\rbrack=120$

The number of positive integers less than 601 that are divisible by 4 and 6

$\lbrack\dfrac{600}{12}\rbrack=50$

The number of positive integers less than 601 that are divisible by 4 and 5

$\lbrack\dfrac{600}{20}\rbrack=30$

The number of positive integers less than 601 that are divisible by 5 and 6

$\lbrack\dfrac{600}{30}\rbrack=20$

The number of positive integers less than 601 that are divisible by 4, and 5, and 6

$\lbrack\dfrac{600}{60}\rbrack=10$

The number of positive integers less than 601 that are divisible by 4 or 5 or 6

$150+100+120-50-30-20+10=280$

The number of positive integers less than 601 that are not divisible by 4 or 5 or 6

$600-280=320$