The LCM and GCF can be difficult concepts to understand because we hear the words in the opposite order of their importance: For example, for the LCM, first we hear "least," then we hear "common," and last we hear "multiple." However, the most important word of the three is "multiple." The multiples of 24 are 1 24, 2 24, 3 24, and so forth, and the multiples of 36 are 1 36, 2 36, 3 36, and so forth. The next-most important word is "common." We are looking for a number that is common to both numbers. The third most important word is the one we hear first, "least."
So the number we want is a multiple, common to both numbers, and the least of all such numbers. This would be the same case for the GCF, for which we want a number that is a factor, common to both numbers, and the greatest of all such numbers. It would be worth taking the time to have a class discussion of the three words when introducing the LCM and GCF.
<< back to Part A: Models for Multiples and Factors