Talk:Least common multiple

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Venn diagram caption

I find the venn diagram caption confusing. It says "a card game which requires its cards to be divided equally among up to 5 players requires at least 60 cards, the number at the intersection of the 2, 3, 4 and 5 sets, but not the 7 set." However, wouldn't any multiple of 5 work? That is 5, 10, 15, 20, etc. It appears to me there is some missing constraint that's not stated and it makes the caption very confusing. Garymm (talk) 14:46, 2 August 2016 (UTC)[reply]

Notice the phrase, "up to 5 players." In other words, the cards must be evenly divisible by 2, 3, 4, and 5. — Anita5192 (talk) 22:01, 2 August 2016 (UTC)[reply]

The product of 2*3*4*5*7=840 not 420. — Preceding unsigned comment added by Gmaauni (talk • contribs) 17:40, 29 January 2019 (UTC)[reply]

True, but the diagram indicates that 420 is the least common multiple of 2, 3, 4, 5, and 7 (which is correct), not the product of all those integers.—Anita5192 (talk) 17:55, 29 January 2019 (UTC)[reply]

Regarding "(and of their combinations, like 6 and 8)": Multiples of 8 are not included in the Venn diagram, as LCM(2,4)=4.— Preceding unsigned comment added by 76.130.156.149 (talk) 15:48, 2 June 2024 (UTC)[reply]

Correct. I have fixed the caption that was also very confusing. D.Lazard (talk) 17:16, 2 June 2024 (UTC)[reply]

Removing C# algorithm

I am about to remove the C# algorithm -- its quite absurd, as one has a much better, smaller, faster algo simply by using Euclid's algorithm to compute gcf, and then compute lcm from gcf. By contrast, the C# algo requires computing the primes first, which strikes me as absurd. Am I missing something? 67.198.37.16 (talk) 16:58, 17 October 2016 (UTC)[reply]

That said, are there algorithms that are particularly space and storage efficient? Naively, computing lcm(a,b) = ab/gcf(a,b) and using Euclid's algo to get gcf(a,b) seems like a pretty good approach, but can one do better? How about the case of lcm(a,b,c) ? or more? 67.198.37.16 (talk) 17:09, 17 October 2016 (UTC)[reply]

Confused

At this part of the page, its confusing: "Once 2 no longer divides, divide by 3. If 3 no longer divides, try 5 and 7." But the table skips 5 and goes right to 7. Please explain? — Preceding unsigned comment added by 2601:602:87F:F80E:5456:C3B9:8127:B90E (talk) 15:42, 30 August 2017 (UTC)[reply]

This page is intended for discussions of how to improve the article and not discussions about the content. Questions such as yours should be asked at Wikipedia:Reference desk/Mathematics. However, to save you the time, the table skips 5 because there are no numbers in the column that are divisible by 5 and you only add a new column when there is some number that is evenly divisible by the prime you are considering. --Bill Cherowitzo (talk) 17:59, 30 August 2017 (UTC)[reply]

Missing definition section about lcm?

I see lots of text explanation and examples but there is no mathematics definition about LCM in this article. Perhaps, we can add a section with the definition of LCM in mathematics language and symbols. Louis925 (talk) 17:44, 25 April 2018 (UTC)[reply]

The least common multiple (LCM) is clearly defined in the lead.—Anita5192 (talk) 18:05, 25 April 2018 (UTC)[reply]

(Edit conflict) It is in the first sentence. While this could be written in symbolic form, that would not be very useful for a reader who is unfamiliar with the concept, as it would take more sophistication to correctly parse the symbolic form than to understand this relatively simple concept. In the spirit of not being overly technical in elementary articles, it is probably best not to include this. --Bill Cherowitzo (talk) 18:13, 25 April 2018 (UTC)[reply]

Equation for finding lcm for more than 2 numbers, this is an example for 3 numbers

Consider to add the following equation, for finding lcm for more than two given numbers, the following example is for given 3 numbers.

\operatorname {lcm} (a,b,c)=\operatorname {lcm} (\operatorname {lcm} (a,b),c)=\operatorname {lcm} (a,\operatorname {lcm} (b,c)).

— Preceding unsigned comment added by Eido95 (talk • contribs) 14:43, 10 November 2018 (UTC)[reply]

I believe you have a good point. The right-hand side,

\operatorname {lcm} (\operatorname {lcm} (a,b),c)=\operatorname {lcm} (a,\operatorname {lcm} (b,c))

, is in the Lattice-theoretic subsection, but the left-hand side, defining

\operatorname {lcm} (a,b,c)

, did not seem to be in the article. I have now added it.—Anita5192 (talk) 18:04, 10 November 2018 (UTC)[reply]