Question

If the least prime factor of 'a' is 3, the least prime factor of 'b' is 7, then the least prime factor of (a+ b) is.

• A. $2$
• B. $3$
• C. $5$
• D. $11$

Answer 1

The correct option is A $2$

Since $7+3=10$. The least prime factor of $a+b$ has to be $2$; unless $a+b$ is a prime number greater than $2$.
Suppose $a+b$ is a prime number greater than $2$. Then $a+b$ must be an odd number. So one of $a$ or $b$ must be an even number. Suppose then that $a$ is even. Then the least prime factor of $a$ is $2$; which is not $3$ or $7$. So $a$ cannot be an even number. Nor can $b$ be an even number. Hence $a+b$ can not be a prime number greater than $2$ if the least prime factor of $a$ is $3$ and $b$ is $7$.
Hence the answer is $2$.