Given two positive integers: a,b

We can find two positive integers: x,y

Such that: lcm(a,b)=xy and x|a , y|b and gcd(x,y)=1

Now if,

f = g (mod a)

Then it is true from any divisor of "a" let x|a then:

f = g (mod x)

Similarly

f = g (mod y)

Note, gcd(x,y)=1 thus,

f = g (mod xy) thus, f = g (mod m)