Question 298967: Suppose a positive integer n is divisible by 21 and by 9. What is the smallest possible number of positive integers that divide n?
A. 3 B. 4 C. 5 D. 6 E. 7
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website! Suppose a positive integer n is divisible by 21 and by 9. What is the smallest possible number of positive integers that divide n?
21 = 3*7 and 9 = 3*3
So the smallest integer divisible by both 21 and 9 is 3*3*7 or 63,
their LCM.
63 is divisible by 1,3,7,9,21, and 63. That's six.
Any other integer divisible by both 21 and 9 will also be
divisible by those 6, and at least one other.
So the answer has to be 6.
Edwin
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