I was just googling problems for this. This is what I found.
When do I use LCM and when do I use GCF?
Do we want to split things into smaller sections?
Are we trying to figure out how many people we can invite?
Are we trying to arrange something in rows or groups?
Do we have an event that will be repeating over and over?
Will we have to purchase or get multiple items in order to have enough?
Are we trying to figure out when something will happen again at the same time?
Shannon is making identical balloon arrangements for a party. She has 32 maroon balloons, 24 white balloons, and 16 orange balloons. She wants each arrangement to have the same number of each color. What is the greatestnumber of arrangements that she can make if every balloon is used?
Bridget has swimming lessons every fifth day and diving lessons every third day. If she had a swimming lesson and a diving lesson on May 5, when will be the next date on which she has both swimming and diving lessons?
Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be the same height?
You are making pumpkin pies for the bake sale. Piecrusts are sold in packages of 3. Pie filling is sold in 4-can packages. What is the least number of piecrusts and filling that you can buy to have the same number of each?
How many of packages of each should you buy?
Thank you very much for this example! It really helped. I have used planets' orbits for LCM as well. I also use an example of three friends wanting to spend their next day off of work together for LCM. One friend works 5 days with one day off, the next 6 days with one day off, and the last 7 days with one day off. If they just enjoyed a day off together, how many days until the time when they can enjoy a communal day off?
I see the hot dog/bun example for explaining real world use of the lcm but I don't understand it. I used prime factorization for 10,8 and end up with lcm = 2x5x2x2 = 40. So 40 is the lcm of 10 and 8. Now if I buy 40 packs of hot dogs that is 400 hot dogs and 40 packs of buns is 320 buns. I am 80 buns shy for my 400 dogs. I don't understand.
I would have missed the principle behind it if you hadn't stated the 400 issue. It's not 400 hotdogs and 400 buns. It's 40 hot dogs and 40 buns. 40/8=5 & 40/10=4. Therefore, it's five packs of hot dogs and four packs of buns.
another good one is something like ...
KSHE radio plays top hits all weekend. They have been playing the new song by "RUcool" every 18 minutes. KDHX has been playing the new song every 24 minutes. If they both play the song at 3:00 PM, when will the next time be that they play the song at the same time?
I do not know but is this correct? Here I found some problems: I see the hot dog/bun example for explaining real world use of the lcm but I don't understand it. I used prime factorization for 10,8 and end up with lcm = 2x5x2x2 = 40. So 40 is the lcm of 10 and 8. Now if I buy 40 packs of hot dogs that is 400 hot dogs and 40 packs of buns is 320 buns. I am 80 buns shy for my 400 dogs. I don't understand.
40 is the number where the hotdog and the buns meet. 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.
They're all (great) examples of LCM. I can't for the life of me think of real world application for HCF/GCF!! (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.)