mersenneforum.org Definition of “common multiple”
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2023-02-04, 22:10   #12
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

37·317 Posts

Quote:
 Originally Posted by drkirkby I note that maxima gives lcm(6,4) as 12 and not 24.
The clue is in the word "common".

12 is a multiple of 4, being 3*4
12 is a multiple of 6, being 2*6

So 12 is a multiple of both 4 and 6 --- it has those factors in common with both of them.

2023-02-04, 23:21   #13
charybdis

Apr 2020

2·52·19 Posts

Quote:
 Originally Posted by drkirkby So when computing the common factors of m and n, you have to factorise m and n if they are not prime? The OU doesn’t say that.
As a1call has mentioned, gcd(m,n) can be found very quickly without factorizing m and n, by using the Euclidean algorithm. Then use lcm(m,n) = mn/gcd(m,n).

2023-02-05, 00:14   #14
Dr Sardonicus

Feb 2017
Nowhere

633810 Posts

Quote:
 Originally Posted by drkirkby Common multiple is not a term that I have come across before, although I have come across least common multiple (lcm).
This statement is self-contradictory. The term "common multiple" is included in "least common multiple."

Discerning the meaning of "common multiple" is merely a matter of knowing two basic definitions. Here, common clearly means "shared." And a multiple of an integer is that integer multiplied by an integer.

Quote:
 Originally Posted by drkirkby But the OU gets a smaller number (12) than multiplying 6 and 4.
Is 12 a multiple of 6? Yes, 12 = 6*2. Is 12 a multiple of 4? Yes, 12 = 4*3. So, 12 is a multiple of both 4 and 6; that is, it is a common multiple of 4 and 6.

2023-02-11, 10:01   #15
drkirkby

"David Kirkby"
Jan 2021
Althorne, Essex, UK

2×229 Posts

Quote:
 Originally Posted by drkirkby So when computing the common factors of m and n, you have to factorise m and n if they are not prime? The OU doesn’t say that. Given that this is a very basic book on maths, not mentioning that seems wrong.
Having read this OU book more, it states that there’s an efficient method, known as Euclid’s algorithm, for finding the lowest common multiple and highest common factors without factorising. So my earlier comment was unfair to the OU. Their material is very good quality.

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