"What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" Is it different from divisible?
What is meant by "evenly divisible"?
20
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elementary-number-theory
terminology
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7It is a school version of "divisible." Used to be fairly common. – 2011-08-19
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3$\rm m\ $ evenly divides $\rm\ n\ $ means simply that $\rm\ n/m\ $ is an integer. The "evenly" presumably means that the remainder upon division is $\:0\:.\:$ – 2011-08-19
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1Subareas of mathematics have their own conventions. Is $-5$ a divisor of $20$? Probably one would be expected to answer yes. What is the sum of the divisors of $20$? Probably one would not be expected to say $0$. It sort of makes sense to qualify divisible, when one means that the quotient is an integer. After all, $5/20=0.25$. But the fact is that in mathematics beyond school mathematics, "evenly divisible" is uncommon. – 2011-08-19
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0This is an interesting problem. Is the answer $\dfrac{20!}{10!}$? I discarded the numbers 1-10. If the number is evenly divisible by multiples, then it is divisible by the number. – 2011-08-20
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1@mathguy80: The problem is just to find the least common multiple of $1, 2, \dots, 20$. Working it out, this is less than $\frac{20!}{10!}$. – 2011-08-20
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0I cleaned up @Andre's comment above, so the display problem should be fixed. So I also removed the discussion pertaining to *that*. – 2011-08-20
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0@Willie Wong: Thank you. Is there anything that I could have done, beside better proofreading? – 2011-08-20
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0@Andre: here's a bit of a 'hack' that sometimes works for me http://meta.math.stackexchange.com/questions/2652/comments-layout-break-if-math-expression-is-too-long/2818#2818 – 2011-08-20
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0@AndréNicolas Actually, it's English rather than "school". Even means, among other things, equal or fair; so an even division is one where every portion is the same and there is no remainder. – 2018-12-08
5 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 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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4$20!$ is not the smallest such number. For example $19!$ already works, and that too is much bigger than needed. – 2013-01-25
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Means the same as "divisible". Answer is $2\times3\times5\times7\times11\times13\times17\times19$.
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1... which is not divisible by $16$, for example. – 2017-04-05