I am a 5th grade teacher and I introduced multiples and factors this week and the kids learned how to find least common multiple and greatest common factor. They get the two confused. Does anyone have any suggestions on helping them to differentiate between the two. Perhaps a catchy saying or song?

One of the things I did when I was the math resource teacher was to break those words down and to explain what each word meant. The reason why they get them confused is because they don't even know what each term means. So, go back, and reteach just LCM. What does least mean? Same with common and multiple. Okay, so least means small, common means the same, and multiple is the product of a number and any other whole number. Now, do many MANY problems to find the LCM. Once they have that down, then do the same for GCF. Break it down, explain what each term means. I found that by breaking it all down, and explaining it, it really helped them.

I always tell them that multiples are skip counting...I make a chart with them as well showing vocab showing that multiples of 24 (for example) are 48, 72, 96.... and factors would be 1, 2, 3, 4, 6, 8, 12, and 24. Then we circle and label GCF and LCM. Just having the visual around which they participated in helps a ton.

LOTS of kids continue to confuse the terms!!! MULTiples are what happen when you MULTIPLY the number by another whole number.

Thank you all. I have tried to break down the terms, but I will review it again this week. I just want to make sure they get it. All your suggestions were very helpful.

Sorry this got so long...was just hard to explain without being able to show visually....sorry! Along that order, when introducing multiples, we play an old children's game called "Squeak" or "Buzz". 1. The students all stand by their desk. 2. You decide what number you are going to do the multiples of...say 3. 3. The first child starts to count with "1", the second says "2", and so on. 4. Each time a multiple of 3 comes up, the child whose turn it is must say "Squeak". If he says the number instead, he must sit down, and the next child says "Squeak". 5. Play continues until you reach a designated goal, say 100. Players still standing could get a small treat or prize. 6. As a variation, the room could be split into two teams or more. Play would be the same, but each time a child fails to say Squeak at the proper time, a mark could be tallied for that team. The team with the least tallies would win the game. That way the children continue to play and learn. It does work great as an anticipatory activity, building interest, and creating a point of reference in remembering the difference between multiples and factors. It is also a great listening and concentrating activity, and is, also, just a lot of fun. When finding LCM, I have them write the numbers being compared with the largest on top. They only write out the multiples for the largest number, stopping to mentally check out the other numbers as they go. 18= 18, 36 4 (4 will not go into 18, so write 2nd multiple, check with 4 again. It goes into 36...LCM of 18 and 4=36) One other thing that I do that has really worked well when factoring, both in helping them to remember which is which and to make sure they get ALL the factors of a number is to have the kids make a T-chart...we call it a factor chart. 1.They place the number to be factored on top of the 't'...say 24. 2.Starting with 1X24, they place the 1 on the left side of vertical line of the T and the 24 directly across on the right side. 1T24 3. They then ask themselves if 2 will go into 24...they place the 2 under the 1 and the 12 under the 24. 4. They do the same with with each digit 1-9, writing down only the ones that when multiplied = 24. 5. Once they have gone through all 9 digits, or the next digit to check is already listed on the other side of the dividing line (ex:6T7 or 4T6 or have double numbers on either side of the dividing line (ex. 7T7; 4T4), they are done. They have not missed any factors and can visually see that they are breaking down the number when they factor it. The factor chart also makes it easy to compare numbers when looking for the GCF...they just do the Factor Charts side by side, circle the factors in common, and choose the largest one.

I have my tutoring student look at this note at the top of his folder: To rename, multiply To reduce, divide

I tell my kiddos that the word multiple is bigger than the word factor... answers for LCM are bigger or equal to than the original number answers for GCF are smaller or equal to the original number

I used the T Chart with my sixth graders yesterday. Love, love, love. Isn't it funny how you get so used to doing something one way that it never occurs to you to try it an easier way?