SOLUTION: Find the smallest possible value of "n" so that 80^n is divisible by 64,100 and 125.

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Question 550557: Find the smallest possible value of "n" so that 80^n is divisible by 64,100 and 125.
Answer by solver91311(24713) About Me  (Show Source):
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The prime factorization of 64 is

The prime factorization of 100 is

The prime factorization of 125 is

So the least common multiple of 64, 100, and 125 is



The prime factorization of 80 is , so you would need at least 3 factors of 80 to have a product with the required 3 factors of 5. And indeed, , obviously divisible by both 64 and 100, is NOT divisible by 125. But is divisible by 125. Hence,


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