Question

Distinct positive integers x and y have 5 and 6 factors respectively. What is the smallest possible product xy if x and y are relatively prime to each other?

a) 10
b) 12
c) 15
d) 18

Answer 1

The smallest possible product xy, given x has 5 factors and y has 6 factors, is 6 when x=2 and y=3.

Step-by-step explanation:

To find the smallest possible product xy, given that x has 5 factors and y has 6 factors, we need to find the smallest pair of distinct positive integers that satisfy these conditions.

In order for x and y to be relatively prime to each other, they must have no common factors other than 1. The only way to achieve this is if x and y are both prime numbers.

The smallest prime numbers that satisfy these conditions are x=2 (with factors 1, 2) and y=3 (with factors 1, 3). Therefore, the smallest possible product xy is 2*3=6.