One negative made us mad, what about two!

e , 2 e \large \color{#EC7300}{-e,}\color{#20A900}{-2e}

Find the lowest common multiple (LCM) of the given above two numbers?

Note: LCM is not just confined to natural numbers.

2 e -2e None of these choices It does not exist e e 2 e 2e

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1 solution

Sravanth C.
May 10, 2015

For solving the LCM of two negative integers, all we need to do is ignore the negative signs and solve it in the way we do it normally, in this case, the numbers are,

e , 2 e \huge \color{#EC7300}{-e,}\color{#20A900}{-2e}

As the LCM is to be found between two irrational numbersm ignore them too, hence we are left with two simple natural numbers, i.e.

1 , 2 \huge \color{#EC7300}{1,}\color{#20A900}{2}

Finding the LCM of 1 , 2 1,2 is as easy as anything. So we come to a con clusion that the LCM is 2 2

Now, one little adjustment will do the work, add the e e back in the answer, so the answer we get is,

2 e \huge \color{#EC7300}{2}\color{#20A900}{e}

Is your question correct ? I don't think we can ever find the LCM of two irraitional numbers .

A Former Brilliant Member - 6 years, 1 month ago

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Please see @Sandeep Bhardwaj sir's IIT foundation class questions, he had posted many.

Sravanth C. - 6 years, 1 month ago

Absolutely perfect sir.

Sravanth C. - 6 years, 1 month ago

Can you plz also expalin why 2 e -2e isn't the answer?

Soumo Mukherjee - 6 years, 1 month ago

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Well , LCM is the smallest positive positive integer divisible by both the integers .

But here instead of integers , we have two irrational nos. So instead of positive integer , our answer will be positive irrational number.

A Former Brilliant Member - 6 years, 1 month ago

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So the integers have to be positive in case of L.C.M because it is implicit in its def?

Soumo Mukherjee - 6 years, 1 month ago

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@Soumo Mukherjee Well , wikipedia states the following :

"In arithmetic and number theory, the least common multiple (also called the lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b.[1] Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.[2] However, some authors define lcm(a,0) as 0 for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility."

So I take back my liberal usage of the word positive and will use non-negative .

A Former Brilliant Member - 6 years, 1 month ago

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@A Former Brilliant Member ....thanks

Soumo Mukherjee - 6 years, 1 month ago

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@Soumo Mukherjee Welcome , and gnight ! TBH I was waiting for your reply since i wasn't satisfied with my reply .

A Former Brilliant Member - 6 years, 1 month ago

2e is not an integer and therefore cannot be the lowest common multiple unless you augment the definition.

Chantry Cargill - 6 years, 1 month ago

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Please read this , it proves the existence of such numbers . . . . . . . .

Sravanth C. - 6 years, 1 month ago

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