Numbers coprime to $30$ up to $100$

From earlier. Numbers divisible by $2$, $3$, or $5$: $74$.

Complement. $100-74=26$.

Conclusion. $26$ integers are coprime to $30$.

Check. Pattern period $30$: $\varphi(30)=8$ per period; $100=3\cdot30+10$. In each full period $8$, so $24$; in the last $10$, coprime to $30$: $1,7,11,13,17,19,23,29$ — but only $1,7$ are $\le10$. So $24+2=26$. ✓