What a coincidence!

Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?

Problem



Consider the arithmetic sequences:

$1998, 2005, 2012, ...$ and

$1996, 2005, 2014, ...$


Which is the next number after $2005$ that appears in both sequences?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.