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There are exactly 77000 ordered quadruples (a,b, c,d) such that gcd (a,b, c,d) =77 and lcm (a,b, c,d) =n, What is the smallest possible value of n?

There are exactly 77000 ordered quadruples (a,b, c,d) such that gcd (a,b, c,d) =77 and lcm (a,b, c,d) =n, What is the smallest possible value of n?
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There are exactly 77000 ordered quadruples (a,b, c,d) such that gcd (a,b, c,d) =77 and lcm (a,b, c,d) =n, What is the smallest possible value of n?

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User Fvannee
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1 Answer

3 votes

Answer: 27,720

Explanation:

This is 2016 AMC 12 B Problem 24. See the attached solution.

There are exactly 77000 ordered quadruples (a,b, c,d) such that gcd (a,b, c,d) =77 and-example-1
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User Rene Zammit
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