Consider the two arithmetic progressions : $$a_1,a_1+d_1,a_1+2d_1,......$$ and $$a_2,a_2+d_2,a_2+2d_2,......$$ where $$a_1$$ and $$d_1$$ are the first term and common difference of first sequence, and $$a_2$$ and $$d_2$$ are the first term and common difference of second sequence.
If we need to find the sequence consisting of the common terms of the two sequences, then we can find the first common term among both. Let it be $$a$$.
The common difference of this sequence will be LCM($$d_1,d_2$$).
So, the sequence having terms as common terms of the two APs will be $$a,a+LCM(d_1,d_2),a+2*LCM(d_1,d_2),......$$.
