His daughters are 8, 3, and 3. The prime factorization of 72 is 2 * 2 * 2 * 3 * 3, so the possible ages are 2, 3, 4, 6, 8, 9, 12, and 18. Using the prime factorization and these numbers the only combinations of numbers that work for the first clue are:

18, 2 and 2.
9, 4 and 2.
6, 6 and 2.
6, 4 and 3.
8, 3, and 3.

Since he doesn’t know the ages after this piece of information the sum of the three numbers must not be unique. The sum of 8, 3, and 3; and 6, 6, and 2 are the same. Now the final clue comes in handy. Since we know that the oldest daughter has her own bed it is likely that she has the bed to herself and is older than the other two so there ages are 8, 3, and 3 rather than 2, 6 and 6.

His daughters are 3, 3, and 8. The prime factorization of 72 is 1 * 2 * 2 * 2 * 3 * 3, so the possible ages are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 ,36. Using the prime factorization and these numbers the only combinations of numbers that work for the first clue are:
1) 1*1*72        2)  1*2*36                  3)  1*3*24                   4)  1*4*18
5) 1*6*12        6)  1*8*9                     7)  2*2*18                   8)  2*3*12
9) 2*4*9          10) 2*6*6                    11) 3*3*8                    12) 3*4*6

The first options is not reasonable, the 2nd also but we proceed. Since he doesn’t know the ages after this piece of information the sum of the three numbers must not be unique
1)  1+2+36=39            2)  1+3+24=28            3) 1+4+18=23
4) 1+6+12=19            5)  1+8+9=18                6)  2+2+18=22
7)  2+3+12=17          8) 2+4+9=15                  9) 2+6+6=14
10) 3+3+8=14           12) 3+4+6=13

Options 9,10 are the same. So now comes the 3rd clue.: there is an older daughter so it must be 8,3,3