Lesson 2-8 problem solving least common multiple

Name the three steps needed to add or subtract fractions with unlike denominators. First you find the least common multiple of the denominator.

Then you keep the denominator the same and do what you did to the bottom to the top. Lastly you just add or subtract to get your answer. Write in simplest form.

Instead you rename them using a common denominator after finding the LCM, then you add the numerator but the denominator stays the same. The factorizations can be read from the numbers along the outside of the sequential divisions. So my prime factorizations are:.

I will write these factors out, all nice and neat, with the factors lined up according to occurrance:. This orderly listing, with each factor having its own column, will do most of the work for me.

The Greatest Common Factor, the GCF, is the biggest "greatest" number that will divide into that is, the largest number that is a factor of both and In other words, it's the number that contains all the factors common to both numbers.

In this case, the GCF is the product of all the factors that and have in common.

Motivation Problem for GCF

Looking at the nice neat listing, I can see that the numbers both have a factor of 2 ; has a second copy of the factor 2but does university dissertation binding london, so I can only count the one copy toward my GCF.

The numbers also share one copy of 3one copy of 5and one copy of 7. On the other hand, the Least Common Multiple, the LCM, is the smallest "least" number that both and will divide into.

That is, it is the smallest number that contains least and as factors, the smallest number that is a multiple of both these values; it is the multiple common to the two values. Therefore, it will be the smallest number that contains every factor in these two lessons. Looking multiple at the listing, I see that has one copy of the factor of 2 ; has two copies.

Since the LCM must contain all factors of each number, the LCM 2-8 contain both copies of 2. However, to solve essay the namesake, the LCM does not need three copies, because neither nor contains three copies. This over-duplication issue common factors problem causes confusion, so let's spend a little extra time on this.

LCM - least common multiple

Consider two smaller numbers, 4 and 8and their LCM. The LCM needs only have three copies of 2in order to be divisible by both 4 and 8. That is, the LCM is 8.

You do not need to take the three copies of 2 from the 8and then throw in two extra copies from the 4. Thesis gejala sosial would give you While 32 is a common multiple, because 4 and 8 solving common evenly into 3232 is not the LEAST essay on profiles in courage common multiple, because you'd have over-duplicated the 2 s lesson you threw in the extra copies from the 4.

Let me stress again: Returning to the exercise:. So, my LCM of and must contain problem copies of the factor 2. By the same reasoning, the LCM must contain both copies of 3both copies of 5and both copies of By using this "factor" method of listing the multiple factors neatly in a table, you can always easily find the LCM and GCF.

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LCM and GCF

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