The Number System 6.NS.B.4
4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Your students have been going steady with math for a while now, and we think it's time they met each other's families. We know meeting the in-laws can be a dreadful experience, but your students and math are going to go the distance, it might as well happen right now.
Yep, it's time to introduce sixth grade students to GCF and LCM—and we aren't talking about your Grandma Catherine Francis or your lanky cousin Marjorie. We're talkin' greatest common factor and least common multiple.
First, students should understand that the concepts of GCF and LCM are all about numbers being connected under the umbrella of multiplication. Students are likely to confuse the two in the very beginning, so we recommend having students review the definitions of each. Twice. At least. And if students are really struggling to remember which is which, remind them that factors are less than or equal to the number we're looking at, and multiples are greater than or equal to that number.
Once they can make lists of factors and multiples for one number, it shouldn't be too much of a stretch to do the same for another number. (Lather, rinse, repeat.) That'll make the GCF and LCM super clear; all they'll have to do is choose either the biggest or the smallest number in both lists.
With finding GCFs and LCMs using lists, it's a simple matter of practice. The more students practice finding factors and multiples and comparing them, the better they'll get. That's no secret. But we suggest getting them nice and comfortable with these lists of factors and multiples before they venture into the big, bad world of the distributive property.
Of course, that means they need to know what on earth the distributive property is first. Without knowing that a(b + c) = ab + ac, nothing else will make sense. After they've got the distributive property in one hand and GCFs in the other, it's time to put those hands together. First, they can find the GCF of two numbers no greater than 100 by writing out the lists. Then, they can express the sum of those two numbers by writing the product of the GCF and the sum of the remaining uncommon factors.
- LCM & GCF
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