Number Theory - Remainders A number is of the form $13k_1+12$ and of the form $11k_2+7$
That is $N = 13k_1 + 12 = 11k_2 + 7$
Now why must N also equal $(13 \times 11)k_3 + 51$ ?
Thanks

Alternately, $N=13k_1+12 = 11k_2+7 \implies N-51 = 13(k_1-3)=11(k_2-4)$  
Thus $N-51$ must be a multiple of both $13$ and $11$.
