If 3 is the least prime factor of number ‘a’ and 7 is the least prime factor of number b, then find the least prime factor of $a + b$ .

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answer is A.

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Detailed Solution

Given that 3 is the least prime factor of number ‘a’ and 7 is the least prime factor of number b.
3 is the least prime factor of number ‘a’.

\Rightarrow

‘a’ is an odd number.
7 is the least prime factor of number b and 2 is a prime number, 2 is not a factor of ‘b’.

\Rightarrow

‘b’ is an odd number.
So, ‘a’ and ‘b’ are odd numbers and the sum of two odd numbers is always even.
That is,

a + b

is an even number.

\Rightarrow a + b

has 2 as a factor.
Since 2 is the least prime number ever and

a + b

has 2 as a factor, the least prime factor of

a + b = 2

.
Therefore, if 3 is the least prime factor of number ‘a’ and 7 is the least prime factor of number b, then the least prime factor of

a + b

is 2.
Hence, option 1 is correct.

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