Question

 Find the smallest prime number that will divide exactly the product of any three consecutive odd integers.

1. 5
2. 3
3. 2
4. 11

Answer 1

Correct Answer - Option 2 : 3

Calculation:

Let the three consecutive odd integers be (2x+1), (2x+3), and (2x+5) respectively.

Now, we want to find out the smallest prime factor of (2x+1) × (2x+3) × (2x+5).

Let us take x =1 then the three consecutive odd integers would be 3, 5 and 7 respectively

Clearly, we have at least one number which is a multiple of 3 in the product (3 × 5 × 7).               

Similarly Let us take x = 2, then the three consecutive odd integers would be 5, 7, and 9 respectively.

Again, we have at least one number which is a multiple of 3 in the product (5 × 7 × 9).                 

So, each product is divisible by 3.

∴ The Smallest prime number that will divide exactly the product of any three consecutive odd integers is 3.