Every 7 years a family has a family reunion. Every 6 years they update their family tree. If they had both in 1997, in what year will both events occur again

Question

Every 7 years the Lancaster family has a family reunion. Every 6 years they update their family tree. If they both had a photo taken and updated their family tree in 1997, in what year will both events occur again

Answer 1

This problem is asking you to find the LCM (least common multiple) of 6 and 7.  Since 7 is prime and does not share any factors with 6, the LCM is 42.  Add that to 1997 and you get 2039 as the next year that both events will occur again.
 
Here is a picture to help understand this:
 
7: 000000X000000X000000X000000X000000X000000X000000X000000X
6: 00000X00000X00000X00000X00000X00000X00000X00000X00000X00
    ^                                                                                         ^
   1998                                                                                   2039