Question

A and B are two positive integers such that the least prime factor of 3 and the least prime factor of B is 5 then the last prime factor of a + b is ​

Answer 1

Answer:

Let a = 3x, b = 5y

Therefore, a + b = 3x + 5y

Observe that both the terms are odd numbers. When you add two odd numbers, the resulting sum will always be an even number. Hence, the least prime factor of a + b is 2

Edit: A lot of people are asking what if x or y are even numbers. Well, if they are, then the least prime factor would be 2 and not 3 or 5 as required by the question. Hence x and y are definitely odd numbers.

Answer 2

Answer:

Given that, a is a positive integer and 3 is the least prime factor of a.

Also, b is a positive integer and 5 is the least prime factor of b.

Since least prime factor of a is 3, it means that a is an odd number.

So, if a is even then 2 is the least prime factor of a.

Similarly, b is also an odd number.

Now, it is known that sum of two odd numbers is an even number.

Hence, a + b will be an even number.