Power of LCM Part 2

Number Theory Level 2

The LCM of 2 & pi is ?

2 2pi None pi

1 solution

Arulx Z
Nov 2, 2015

If LCM of 2 and $\pi$ exists, then there exists an integer $x$ such that $2 \times x = a\pi$ where $a$ is any integer. But since 2 and $x$ are both integers and product of two integers will always be an integer, no value of $x$ exists such that $2x$ is irrational. In other words, integer set is closed under multiplication.

Moderator note:

It is not true that "LCM must be a positive integer". For example, the LCM of $2 \pi$ and $3 \pi$ is simply $6 \pi$ .

LCM just means "least common multiple". So you list out all of the multiples of a number, we want to see if they have a common multiple, and then find the least (positive) one.

@Calvin Lin I have edited the question accordingly. Please check whether my new answer is correct or not.

Arulx Z - 5 years, 7 months ago

Yup, this is much better. You should be careful and clarify that we want the smallest positive multiple, which is why 0 isn't considered the LCM.

Calvin Lin Staff - 5 years, 7 months ago

Power of LCM Part 2

1 solution

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