What is the smallest composite number that is divisible by no prime less than or equal to 19?
A) 674
B) 361
C) 667
D) 657
E) 399

Question

What is the smallest composite number that is divisible by no prime less than or equal to 19? ​
A) 674
B) 361
C) 667
D) 657
E) 399

Quizplus · Accepted Answer

To be divisible by no prime less than or equal to 19, the number must be divisible by all primes greater than 19. The primes greater than 19 are 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. The smallest composite number that is divisible by all of these primes is their product, which turns out to be 667.

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