SOLUTION: Let n be a positive whole number that is divisible by both 18 and 8. What is the smallest number of positive whole numbers that divide n?

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Question 850909: Let n be a positive whole number that is divisible by both 18 and 8. What is the smallest number of positive whole numbers that divide n?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
18=2%2A9=2%2A3%5E2
8=2%5E3
The least common multiple of 18 and 8 is
2%5E3%2A3%5E2=8%2A9=72 .
So n is 72 or a multiple of 72 .
72=2%5E3%2A3%5E2 has
%283%2B1%29%2A%282%2B1%29=4%2A3=highlight%2812%29 factors,
that can be written as
2%5Ea%2A3%5Eb where
a can be 0, 1, 2, or 3,
and b can be 0, 1, or 2.
The number of positive whole numbers that divide 72 is 12%29 ,
and no multiple of 72 could have less factors, so the smallest number of positive whole numbers that divide n is
highlight%2812%29 .