SOLUTION: the product of any two of the numbers 40,62,and z is divisible by the third.what is the smallest possible integer z with this property?

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Question 364747: the product of any two of the numbers 40,62,and z is divisible by the third.what is the smallest possible integer z with this property?
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
40%2Az%2F62 must be a positive integer, which means 20%2Az%2F31 must be a
 positive integer, so z must have factor 31.

62%2Az%2F40 must be a positive integer, which means 31%2Az%2F20 must be a
 positive integer, so z must have factor 20.

So the smallest integer that meets those two conditions is 31×20 or 620

Now let's see if 620 meets the third condition

%2862%2A40%29%2Fz or 2480%2Fz must be a positive integer, and since

2480%2F620 = 4, 620 meets all 3 requirements so we know that 620 is the answer.

Edwin