SOLUTION: What is a number that is a multiple of 2 and 7, is less than 100 but greater than 50 and the product of three different prime numbers?

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Question 995937: What is a number that is a multiple of 2 and 7, is less than
100 but greater than 50 and the product of three different
prime numbers?

Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
2*7*5 = 70.

The solution is unique.


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
She beat me to it, but she didn't bother to explain how to 
get the answer.

What is a number that is a multiple of 2 and 7, is less than
100 but greater than 50 and the product of three different
prime numbers?
2 and 7 are primes, so those have to be two of the primes
of which the required number is the product of, so we need 
another prime p so that our number is 2*7*p

  50 < 2*7*p < 100

   50 < 14p < 100

Divide through by 14

3.57... < p < 7.14...

The only prime different from 2 and 7
between those two values is 5.

So p = 5

The number is therefore 2*7*p = 2*7*5 = 70.

Edwin