Deciding whether to use common multiples or common factors to solve problems can be tricky. Therefore to remember:
GCF
problems involve sharing/dividing evenly
LCM problems involve things
happening in cycles/ same time
Here's a sample problem:
There are 40 girls and 32 boys who want to participate on co-ed soccer intramural teams. If each team must have the same number of girls and the same number of boys, what is that greatest number of teams that could participate? How many boys will be on each team? How many girls on each team?
Think about what you are being asked to do with the values you are given. In this case you are being asked to divide/split your numbers into equal groups. This is your hint to begin to find factors. Best practice is to use the u-turn method to ensure that you find all the factors of a number in an organized manner. When the problem asks for the "greatest" number it is asking for the greatest common factor (GCF). Keep in mind greatest doesn't mean multiple even though multiples create larger and larger numbers. Also be sure you are answering what is being asked. Even though you may have found the GCF, you have to use it to answer the rest of the questions
Here's another sample:
Ms. Pearl is shopping at the supermarket. She is getting things for the sandwiches she is going to prepare for next Sunday's picnic. She sees that hamburger buns come in packs of 8 but the hamburgers themselves come in packs of 10. What is the least number of packs of buns and burgers she should get so she has an equal number of buns and burgers?
For this problem you will need to find multiples because it only makes sense that you will be increasing the number of packs to be able to get equal numbers. Because it is asking for the least number of packs you will be finding least common multiple (LCM). However, the LCM only tells you the number of buns and hamburgers (which is 40 in this case) so you will have to use it to determine the number of packs of each type of item.
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