SOLUTION: What is the smallest odd number you can obtain from the product of four different prime numbers? Show or explain how you got your answer.

Question 591789: What is the smallest odd number you can obtain from the product
of four different prime numbers? Show or explain how you got
your answer.

Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The product of any two odd numbers is odd:

.

Since

is even, hence

is odd.

Any product that has a factor of 2 is even, so in order to get 4 prime factors of an odd number, 2 must be excluded. The smallest product is therefore obtained from the next four prime numbers.

John

My calculator said it, I believe it, that settles it

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Cannot use 2, because 2 is even and the product of an even number with any set of integers is even.

Therefore, use the next four smallest primes, 3,5,7,11 and multiply them.
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