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Suppose $a$ and $b$ are positive integers such that the units digit of $a$ is $2$, the units digit of $b$ is $4$, and the greatest common divisor of $a$ and $b$ is $6$. What is the smallest possible value of the least common multiple of $a$ and $b$?

 Jun 27, 2018

Best Answer 

 #1
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Here are a couple of candidates:

a =12 and  b=54

GCD[12, 54] =6

LCM[12, 54] =108

Also a =42 and b= 24 will give the same GCD of 6, but the LCM[42, 24] =168 which is > than the first one.

 Jun 27, 2018
 #1
avatar
+1
Best Answer

Here are a couple of candidates:

a =12 and  b=54

GCD[12, 54] =6

LCM[12, 54] =108

Also a =42 and b= 24 will give the same GCD of 6, but the LCM[42, 24] =168 which is > than the first one.

Guest Jun 27, 2018

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