What is meant by "evenly divisible"?

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"What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" Is it different from divisible?

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6 Answers

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Evenly divisible means that you have no remainder. So, 20 is evenly divisible by 5 since 20 / 5 = 4. Though, 21 is not evenly divisible by 5 since 21 / 5 = 4 R 1, or 4.2.

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evenly divisible = divisible .

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Evenly divisible is same as divisible. So, you are just looking for the L.C.M. of first $20$ natural numbers.

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"Evenly divisible" is equivalent to the term ``divides.''

For example, we can say that "20 is evenly divisible by 5", which is equivalent to saying that "5 divides 20"; or in mathematical notation, $5 | 20$.

I am sure that the author of the question that you cite, "What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" chose to use the term "evenly divisible" instead of the more ordinary "divides", because to opt for the latter one would need to say something long-winded like, "1|n" and $2|n$ and \ldots and $20|n$, where $n$ is the smallest such integer in question.

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Evenly divisible would mean that the number is divisible by any number completely. To answer your question, the correct answer is 20! (20 factorial).

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Means the same as "divisible". Answer is $2\times3\times5\times7\times11\times13\times17\times19$.

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