Find the smallest four digit number which is divisible by $15,25,40$ and $75$

Question

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).

Answer 1

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 $1200$.

Answer 2

LCM of $15,25, 40 , 75$

will be $600$

The smallest $4$ digit number is $1000$;

Now find the multiple of $600$ close to $1000$.

Hence it's answer is $1200$

Answer 3

You're doing it right.

You just need the smallest multiple of $600$ that has four digits, and that is $1200$