Suppose we have a number X, and we need to find the modulus of it with N numbers, A₁, A₂, ..., A_N.

Then is it true that if we know the modulus of X when divided by LCM(A₁, A₂, ..., A_N), then we can know the individual remainders when X is divided by these numbers (A₁, A₂, ..., 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.