What is the smallest positive multiple of $13$ that is greater than $500?$
I know that a multiple of $13$ is of the form $13k$, where $k$ is a positive integer. To find the smallest multiple of $13$ that is greater than $500$, I need to find the smallest $k$ such that $13k > 500$. I can start by dividing $500$ by $13$ to get an estimate of $k$. I get $500 \div 13 \approx 38.46$. This means that $k = 38$ is too small, since $13 \times 38 = 494 < 500$. But $k = 39$ is large enough, since $13 \times 39 = 507 > 500$. So the smallest positive multiple of $13$ that is greater than $500$ is $13 \times 39 = 507$. 