[Numeracy 124] Re: introductions
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Tue Feb 9 00:03:39 EST 2010
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> Carolyn writes:
> Suppose the numbers are 15 and 21. The LCD would be 3: 15 = 3 * 5;
> 21 = 3 * 7. The number they have *in common* is 3.
3 is the Greatest Common Factor: GCF, not the Lowest Common
Denominator: LCD
> Suppose the numbers are 49 and 98. The LCD would be 49: 49 = 7 * 7;
> 98 = 7 * 7 * 2. The numbers they have *in common* are 7 and 7, and 7
> * 7 = 49.
The Lowest Common Denominator would be 98
The Lowest Common Denominator is used to create equivalent fractions
for the purpose of adding and subtracting fractions with like
denominators... ( same size pieces)
Equivalent fractions are fractions in "higher terms" than the original
fractions.
I think there is confusion among: Least Common Denominator, Least
Common Multiple, and Greatest Common Factor.
The Least Common Denominator is the same as the Least Common Multiple.
It is called the Least Common Denominator when it is serving as the
denominator of equivalent fractions that have been created in order to
create the "same size pieces" so they can be added or subtracted .
The "new" denominator is always either the larger of the original
denominators ( if the smaller one is a factor if it) or larger than
the original ones.... thus is is a common multiple of the two
original denominators. Barbara's example, a few posts ago....
illustrated this.
Otherwise, when NOT serving as a DENOMINATOR of a fraction, the
lowest multiple that two ( or more) numbers have in common is called
the Least Common Multiple. It is CONTEXT that changes the scenery
here and it is called by a different name depending on the context. .
> Try 45 and 21 for the LCM. What is the smallest number that is a
> multiple of both numbers? 45 = 3 * 3 * 5, 21 = 3 * 7. The LCM = 3 *
> 3 * 5 * 7 or 105. (Each number has a 3, so the first three only
> counts once. There is an extra 3 in 45, plus the 5. 21 still has a
> 7. Multiply all those together.
> Or let's try 15 and 49. 15 = 3 * 5, 49 = 7 * 7. No numbers in
> common, so multiply them all together. LCM = 3 * 5 * 7 * 7 or 735.
Carolyn's example above is an example of finding the Least Common
Multiple ( sometimes known as Lowest Common Denominator) by using
Prime Factorization.
Maureen Carro, MS, ET
Academic Learning Solutions
Alamo, CA
mcarro at lmi.net
On Feb 8, 2010, at 3:18 PM, Carolyn Dickinson wrote:
> What is the difference between the Lowest (or least) Common
> Denominator and the Least Common Multiple and what different
> functions do they accomplish?
>
> The LCD is the smallest number that will go INTO each of the
> numbers, while the LCM is the smallest number that each of the
> numbers will divide into (the smallest number that is a multiple of
> both numbers).
>
> Suppose the numbers are 15 and 21. The LCD would be 3: 15 = 3 * 5;
> 21 = 3 * 7. The number they have *in common* is 3.
> Suppose the numbers are 49 and 98. The LCD would be 49: 49 = 7 * 7;
> 98 = 7 * 7 * 2. The numbers they have *in common* are 7 and 7, and 7
> * 7 = 49.
>
> Try 45 and 21 for the LCM. What is the smallest number that is a
> multiple of both numbers? 45 = 3 * 3 * 5, 21 = 3 * 7. The LCM = 3 *
> 3 * 5 * 7 or 105. (Each number has a 3, so the first three only
> counts once. There is an extra 3 in 45, plus the 5. 21 still has a
> 7. Multiply all those together.
> Or let's try 15 and 49. 15 = 3 * 5, 49 = 7 * 7. No numbers in
> common, so multiply them all together. LCM = 3 * 5 * 7 * 7 or 735.
>
> Does that help?
>
> Carolyn Dickinson
> Western Nebraska Community College
> Scottsbluff, Nebraska
>
> On Sat, Feb 6, 2010 at 12:56 PM, George Demetrion
> <gdemetrion at msn.com> wrote:
>
> Good afternoon all.
>
> While I am an experienced adult educator I am a newbie math teacher,
> but I'm plugging away in my first transitions to college basic math
> course.
>
> We've had two three hour sessions thus far in a 15 week course and
> things are moving along okay.
>
> To be sure I've put a lot of time practicing my math through basic
> algebra and concentrating on the assignments in our weekly sessions.
>
> I'm learning and I'm also getting a good experiential dose of math
> phobia, which in turn, in the process of transforming in the process
> of learning and then drawing on my overall teaching skills,
> especially incorporating basic explanation, a lot of practice and
> collaborative scaffolding instructional processes.
>
> One technical question:
>
> What is the difference between the Lowest (or least) Common
> Denominator and the Least Common Multiple and what different
> functions do they accomplish?
>
> Keep it simple and straightforward, please.
>
>
> George Demetrion
> East Hartford, CT
>
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>
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