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Number Theory: Least Common MultiplesT Cyan 5.1.2CR To find the multiples of a number, skip count the number! 3, 6, 9, 12, 15 and so on are the multiples of three, an infinite sequence. 5, 10, 15, 20 . . . are the multiples of five. Their least common multiple (LCM), then, is 15. Two friends will need: Cuisenaire® rods,S cm grid, two dot dice, and a meter stick. Younger student, array rods from 1 cm to 10 cm in length. Roll the dice; place a corresponding rod alongside the meter stick, one end at zero. Form a row of same-color rods along the meter stick as far as you can? Record the multiples with commas. Older student, take a turn—If you get the same dot set as your friend, roll again? If you roll eleven or twelve, choose one dot set? Both students, take turns until you find common multiples —and then a least common multiple—the smallest common to two sequences. With a teacher,T write about LCMs. Repeat twice? T-Note: Such activities as this build images of multiple sequences. The closer to concrete these images are, the easier it will be to recall LCMs as well as greatest common factors (GCFs) –both important for operations with fractions. Swww.etacuisenaire.com M1-4212A [6-tray set of rods] NCTM N&O 2 ©2012 NDS