Suppose we have a number *X*, and we need to find the modulus of it with *N* numbers, *A*_{1}, *A*_{2}, ..., *A*_{N}.

Then is it true that if we know the modulus of *X* when divided by *LCM*(*A*_{1}, *A*_{2}, ..., *A*_{N}), then we can know the individual remainders when *X* is divided by these numbers (*A*_{1}, *A*_{2}, ..., *A*_{N}).

Can anyone give me a proof? And also the method of how to find the individual remainders.

I read this on a editorial on HackerEarth.