# Application of lcm and gcf

KDHX has been playing the new song every 24 minutes. If they both play the song at 3: Here I found some problems: So basically it means that u need to buy x number of hotdogs which is 4 and y number of buns which is 5. So the ans is 4 packs of hotdogs and 5 packs of buns. Simplifying fractions is not real world and kids quickly spot it's quicker to divide by 2 then 2 then 3 than calculate that the HCF is 12 and then divide.

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## LCM & GCF Examples

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I posted this on the Math board, but since I teach fifth grade, I hope my fifth grade colleagues will help me! Funny , I was just googling problems for this. This is great, thank you. Hot dogs , Hot dogs and buns are an example I always use. That hot dog bun is a perfect example of real-life application!

## Why are we learning Greatest Common Factor (GCF)?

Thank you parker! I present GCF as a tool for simplifying fractions. Guest , Thank you very much for this example! Anonymous T. Another use , Students find GCF all the time when reducing fractions. Thank you SO much, this really helped me! Hot Dogs and Buns , Search "Father of the Bride" on YouTube.

I don't understand , I understand now , I would have missed the principle behind it if you hadn't stated the issue. 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.

LCM and GCF word problems

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. 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 2 , but does not, so I can only count the one copy toward my GCF. The numbers also share one copy of 3 , one copy of 5 , and 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 both 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 numbers. Looking back at the listing, I see that has one copy of the factor of 2 ; has two copies.

However, to avoid overduplication, the LCM does not need three copies, because neither nor contains three copies.

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This over-duplication issue with factors often causes confusion, so let's spend a little extra time on this. Consider two smaller numbers, 4 and 8 , and their LCM.

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The LCM needs only have three copies of 2 , in 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 8 , and then throw in two extra copies from the 4. This would give you While 32 is a common multiple, because 4 and 8 both divide evenly into 32 , 32 is not the LEAST smallest common multiple, because you'd have over-duplicated the 2 s when you threw in the extra copies from the 4.

Let me stress again: Returning to the exercise:. So, my LCM of and must contain both copies of the factor 2. By the same reasoning, the LCM must contain both copies of 3 , both copies of 5 , and both copies of By using this "factor" method of listing the prime factors neatly in a table, you can always easily find the LCM and GCF. Completely factor the numbers you are given, list the factors neatly with only one factor for each column you can have 2 s columns, 3 s columns, etc, but a 3 would never go in a 2 s column , and then carry the needed factors down to the bottom row.

For example,. At the heart of math education is problem solving.

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