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.

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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) About Me  (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

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Answer by richard1234(7193) About Me  (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.