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If \(a\) and \(b\) are positive integers such that \(\gcd(a,b)=210\), \(\mathop{\text{lcm}}[a,b]=210^3\), and \(a , how many possible values are there for \(a\)?

 Sep 15, 2020
 #1
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Sorry, typo. \(a

 Sep 15, 2020
 #2
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What does \(a  mean in LaTex?

 Sep 15, 2020
 #3
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a

for some reason it was formatted wrong.

Guest Sep 15, 2020
 #4
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a and b are the same as their GCD and LCM. In other words:

 

GCD(210,  210^3) = 210, and 

LCM(210,  210^3) = 210^3. If "a" stands for 210, then "a" can only take one value of 210. If you double it, say to 420, then the new GCD = 420....and so on.

 Sep 15, 2020
 #5
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So what is the answer?

Guest Sep 15, 2020

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