How to find one unknown number while LCM and GCD is given?

Question

help me find unknown integer number n such as

LCM(n,50) = 200

and

GCD(n,50) = 10

how do you solve?

I tried factoring each numbers such as

$200 = 2^3*5^2$

$10 = 2*5$

$50 = 2 * 5^2$

but idk whats next...

edit:

ok thanks for the help I am now able to solve this type of question:) thanks a lot!

answer on note

Answer 1

$\frac{ab}{GCD(a,b)}=LCM(a,b)$

Thus the answer is $n=40$