A7. The product of five different integers is 12 . What is the largest of the integers?
Solution
3

The smallest product of five different positive integers is $1 \times 2 \times 3 \times 4 \times 5=120$. Therefore, at least one of the integers in this case is negative. Also, as the product of the integers is positive, the number of negative integers amongst the five different integers is even. The smallest positive product of four different integers is $-2 \times-1 \times 1 \times 2=4$. So the only five different integers whose product is 12 are $-2,-1,1,2$ and 3 .