1. Using Factor Trees to find the least common multiple (LCM)

2. Least Common Multiple
The least common multiple of two (or more) numbers is the smallest number that can be divided by both (or all) the numbers.
Example the LCM of 4 and 7 is 4x7 = 28

3. Finding the LCM
To find the LCM we can list all the multiples of each number and find the first one that appears in each list
Eg LCM 24 and 36
24, 48, 72, 96,
36, 72, 108,
So the LCM of 24 and 36 is 72

4. But, if you have big/nasty numbers
This is takes ages
Easy to make a mistake

5. LCM – Using Factor Trees

6. Find the LCM of 45 and 72
First write each number as a product of its primes
Find the Highest Common Factor by identifying the primes which appear in both numbers
Find the Lowest Common Multiple by multiplying the Highest Common Factor by all the factors that are leftover.
HELP!!

7. 1. Product of Primes 45 72 3 x 3 x 5 = 45 2 x 2 x 2 x 3 x 3 = 7236 5 9 2 18 3 3 2 9
3 x 3 x 5 = 45
32 x 5 = 45
2 x 2 x 2 x 3 x 3 = 72
23 x 32 = 72 3 3

8. 2. Highest Common Factor HCF = 3 x 3 = 9 45 72 72 45 2 36 5 9 2 18 3 3

9. 3. LCM = HCF x Leftovers HCF = 3 x 3 = 9 Leftovers = 5 x 23 = 4045 45 3 9 5 72 72 2 36 18 3 9
HCF = 3 x 3 = 9
Leftovers = 5 x 23 = 40
LCM = 9 x 40 = 360

10. Find the HCF and then LCM of the following:90
108 70
165
168
210
1400
756