The Notion of LCM

$\bullet$ LCM of any two non-zero rational numbers always exists.

$\bullet$ LCM of any non-zero rational and any irrational number never exists.

$\bullet$ LCM of any two irrational numbers may or may not exist.

$\bullet$ Also you can start out the discussion here on this note through comments.

Till then you can try to solve the set of such problems : IIT Foundation Classes

#NumberTheory #JEE #IITJEE #SandeepBhardwaj #BrilliantClasses

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

What is so cool about LCMs?

Agnishom Chattopadhyay - 6 years, 1 month ago

What are the conditions for two irrational numbers to have an LCM?

Sharky Kesa - 6 years, 1 month ago

According to my understanding :

LCM of two like irrational numbers always exists.

Now what I mean to say like here is :

Let any irrational number being $\lambda$ . then another irrational number $\alpha$ will be like to $\lambda$ if $\alpha=A \times \lambda$ where $A$ is any non-zero rational number.

Sandeep Bhardwaj - 6 years, 1 month ago

Sir, but what about this and this.

Sravanth C. - 6 years, 1 month ago

@Sravanth C. – Yeah, LCM exists in both the cases. in one case LCM is $6\pi$ and in the other case LCM is $2e$ .

Sandeep Bhardwaj - 6 years, 1 month ago

@Sandeep Bhardwaj – Thank you very much sir, I was scared that my question was wrong! I love you sir! :P $\huge \ddot \smile$

Sravanth C. - 6 years, 1 month ago

@Sravanth C. – Thank you my dear, $\huge \ddot \smile$

Sandeep Bhardwaj - 6 years, 1 month ago

@Sandeep Bhardwaj – BTW, How were the questions sir?

Sravanth C. - 6 years, 1 month ago

@Sandeep Bhardwaj – Sir U gave away the answer

Rajdeep Dhingra - 6 years, 1 month ago

But Sir i thought in your previous questions there are no LCM for two irrational numbers nor between irrational number and rational number.

Hafizh Ahsan Permana - 6 years, 1 month ago

Yeah, I would Like to Know the same. :)

Mehul Arora - 6 years, 1 month ago

What is the most accepted definition of LCM sir, which is in accordance with all integers, rationals and irrationals ? (As you may have known, most people like me are having a problem with the definition ).

Thanks in advance :).

Venkata Karthik Bandaru - 6 years, 1 month ago

Can you post questions on Polynomials ? and Geometry ?

Rajdeep Dhingra - 6 years, 1 month ago

Good explanation about LCM'S keep it up::)

Kutumbaka Jaswanth - 6 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$