A number is divisible by $4$ and $6$. Can you say that the number is divisible by $24$? Justify.

A number is divisible by $8$ and $9$. Can you say that the number is divisible by $72$? Justify.

Write a number which is divisible by $3$ and $6$ but not by $18$.

Write a number which is divisible by $4$ and $8$ but not by $32$.

Write a number which is divisible by $6$ and $15$ but not by $90$.

Find the smallest number which should be added to $43216$ to make it divisible by $6$.

Replace $*$ by the largest digit to make $724*24$ divisible by $8$.

Replace $*$ by the largest digit to make $724*24$ divisible by $9$.