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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

Note by Sandeep Bhardwaj
2 years, 2 months ago

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What is so cool about LCMs? Agnishom Chattopadhyay · 2 years, 2 months ago

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Can you post questions on Polynomials ? and Geometry ? Rajdeep Dhingra · 2 years, 2 months ago

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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 :). Karthik Venkata · 2 years, 2 months ago

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What are the conditions for two irrational numbers to have an LCM? Sharky Kesa · 2 years, 2 months ago

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@Sharky Kesa 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 · 2 years, 2 months ago

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@Sandeep Bhardwaj 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 · 2 years, 2 months ago

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@Sandeep Bhardwaj Sir, but what about this and this. Sravanth Chebrolu · 2 years, 2 months ago

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@Sravanth Chebrolu Yeah, LCM exists in both the cases. in one case LCM is \(6\pi\) and in the other case LCM is \(2e\). Sandeep Bhardwaj · 2 years, 2 months ago

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@Sandeep Bhardwaj Thank you very much sir, I was scared that my question was wrong! I love you sir! :P \(\huge \ddot \smile\) Sravanth Chebrolu · 2 years, 2 months ago

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@Sravanth Chebrolu Thank you my dear, \(\huge \ddot \smile\) Sandeep Bhardwaj · 2 years, 2 months ago

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@Sandeep Bhardwaj BTW, How were the questions sir? Sravanth Chebrolu · 2 years, 2 months ago

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@Sandeep Bhardwaj Sir U gave away the answer Rajdeep Dhingra · 2 years, 2 months ago

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@Sharky Kesa Yeah, I would Like to Know the same. :) Mehul Arora · 2 years, 2 months ago

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Good explanation about LCM'S keep it up::) Kutumbaka Jaswanth · 2 years, 2 months ago

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