It is proved that any three digit can be written twice to get a six digit, which can be divided by 7, 11 and 13 at the same time

It is proved that any three digit can be written twice to get a six digit, which can be divided by 7, 11 and 13 at the same time


abcabc=abc*1001
1001=7*11*13
therefore
abcabc=abc*7*11*13
Can be divided by them at the same time