Exponential L.C.M.

Number Theory Level 2

$\huge \color{#D61F06}{1}, \color{#20A900}{e}$

Find the lowest common multiple (L.C.M.) of the given above two numbers ?

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L.C.M. does not exist. None of the above. 1 e

2 solutions

Abhishek Sharma
May 8, 2015

If LCM of $a$ and $b$ is $L$ , then $L=a\times n=b\times m$ where $n$ and $m$ are integers.

Now if LCM of $1$ and $e$ exists then $e=\frac{n}{m}$ . But this can't be true as $e$ is an irrational number and $\frac{n}{m}$ is rational. Our assumption was wrong therefore LCM of $1$ and $e$ does not exist.

Samrit Pramanik
May 8, 2015

This is because $e$ is an irrational number.

Exponential L.C.M.

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2 solutions

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