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2018 AMC 10A Problem 22

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2018 AMC 10A Problem 22AMC 10 Step by Step
Name:                             Date: September 13, 2026
GCD & LCM · difficulty 4 of 5 · about 6 min · position P21-25

Let a,b,c,a, b, c, and dd be positive integers such that gcd⁡(a,b)=24\gcd(a, b)=24 , gcd⁡(b,c)=36\gcd(b, c)=36 , gcd⁡(c,d)=54\gcd(c, d)=54 , and 70<gcd⁡(d,a)<10070<\gcd(d, a)<100 . Which of the following must be a divisor of aa ?

  1. A)

     5\text{ 5}

  2. B)

     7\text{ 7}

  3. C)

     11\text{ 11}

  4. D)

     13\text{ 13}

  5. E)

     17\text{ 17}

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