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LCM(2,5) = 10 so they will meet every 10 days. Now, "in the next 30 days" is Day 2 to Day 31. If they met on Day 1, then they will meet again on Day 11, 21 and 31 (every 10 days). Answer: They will meet 3 more times in the next 30 days. Pictorial representation 1 2 3 4 5 6 7 8 9 10 K K K K K C C 11 12 13 14 15 16 17 18 19 20 K K K K K C C 21 22 23 24 25 26 27 28 29 30 K K K K K C C 31 K C

They meet on the first day of the month, this means
day 2 for Kevin = day 5 for cousin
So the other days they meet would be the highlighted days which coincides.
Multiples of 2 <=30 —> 2, 4, 6 , 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
Multiples of 5 <= 30 —> 5, 10, 15, 20, 25, 30
Answer: They will meet 3 more times in the next 30 days.

Nice. Just wondering… is there anyway to solve this problem without drawing out the days? I guess not.