Find the smallest four digit number which is divisible by $15,25,40$ and $75$ I'm stuck on this question. My working:
\begin{align*}
15 & = 3 \cdot 5\\
25 & = 5^2\\
40 & = 2^3 \cdot 5\\
75 & = 3 \cdot  5^2
\end{align*}
LCM $= 600$
And I'm not sure what to do after this (if the above steps are right). 

The answer is $\boxed{1200}$. Following your method, we have
$$15 = 3 \cdot 5 \\ $$
$$25 = 5^2 \\$$ 
$$40 = 5^1 \cdot 2^3 \\$$
$$75 = 3 \cdot 25 $$
Thus, to find the LCM, we take the maximum exponents for each of the prime factors, and we obtain $600$. But, since we need a four-digit number, we can multiply by $2$ to obtain $1200$.
