Vocabulary Multiples Common multiples A number times 1, 2, 3, 4 etc. ex: 6, 12, 18, 24, ...are multiples of 6 Common multiples Multiples that two or more numbers share. ex: 24 and 48 are multiples of both 12 and 24

Least common multiple (LCM) The smallest common multiple of two or more numbers ex: 24 is the LCM of 6 and 8 30 is the LCM of 5 and 6 There is no Greatest Common Multiple… Why not?

Ways to find LCM 1. Make lists of the multiples: 9: 9, 18, 27, 36, 45, 54, ... 15: 15, 30, 45, 60,... 2. Make factor trees circle the most that any prime factor appears: 24 = 2(2)(2)(3) 30 = 3(2)(5) LCM = 2(2)(2)(3)(5) = 120

There are four 2’s in 48 and two 3’s in 36 (2)(2)(2)(2)(3)(3) = 144! How to use factor trees to find the LCM Look for the most prime factors in either tree… There are four 2’s in 48 and two 3’s in 36 (2)(2)(2)(2)(3)(3) = 144!

Ways to find LCM (3)(2)(2)(3)(2)(2) = 144 3. Use a Venn diagram: 36 48

Ways to find LCM (2)(3)(2)(3)(4) = 144 4. Use a ladder: 36 48 18 24 6