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

(a) 2
(b) 3
(c) 5
(d) 10

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Solution

Since

The least prime factor of has to be 2; unless is a prime number greater than 2.

Suppose is a prime number greater than 2. Then must be an odd number

o 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 can not be an even number nor can b be an even number. Hence can not be a prime number greater than 2 if the least prime factor of a is 3 and b is 7.

Thus the answer is 2.

Hence the correct choice is (a).

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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 (a) 2 (b) 3 (c) 5 (d) 10

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

(a) 2
(b) 3
(c) 5
(d) 10