The product of three different positive integers is 144 . What is the maximum possible sum of these three integers?
(A) 20
(B) 75
(C) 146
(D) 52
(E) 29
For the sum to be a maximum, we try to use the largest divisor possible.

Although 144 is the largest divisor, using it would require that the remaining two divisors both equal 1 (since the divisors are integers).

Since the question requires the product of three different divisors, $144=144 \times 1 \times 1$ is not possible and the answer cannot be $144+1+1=146$ or (C).

The next largest divisor of 144 is 72 and $144=72 \times 2 \times 1$.

Now the three factors are different and their sum is $72+2+1=75$.

Since 75 is the largest possible answer remaining, we have found the maximum.

ANswer: (B)