I have the following congruencies: $$x= 4(mod 7) $$ $$x= 2(mod 4) $$ $$x= 2(mod 5) $$
I solved for the smallest possible x that satisfies all of those conditions by breaking it up like so: $$a= 4(mod 7) $$ $$a= 0(mod 4) $$ $$a= 0(mod 5) $$ which gets a = 60
$$b= 0(mod 7) $$ $$b= 2(mod 4) $$ $$b= 0(mod 5) $$ which gets b = 70
$$c= 0(mod 7) $$ $$c= 0(mod 4) $$ $$c= 2(mod 5) $$ which gets c = 112
then I do $$ a + b + c = 242 $$
But it says the answer is 102.
I tried it like this too: https://www.youtube.com/watch?v=zIFehsBHB8o and got the same answer.
What am I doing wrong?