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# LCM/GCD Number Problem

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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
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