1. 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

2. 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?

3. 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) = 3(2)(5)
LCM = 2(2)(2)(3)(5) = 120

4. 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!

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

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