If (p,q) = p,
then p\mathrel{∣}q
and q
is a multiple of p.
Problem 66
We want the least common multiple of 6 and 10. The nights off
intersect every 30 days. July has 31 days, so by this method their next
shared day off is the 31^{st}. On the “trick question” side, though, they may
have July 4^{th} off together\mathop{\mathop{…}}
Problem 70
Here we need the greatest common divisor, (60,72) = 12.
So the longest common length is 1 foot.