Least Common Multiple

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

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

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, 120 . . .

• 36, 72, 108, 144 . . .

• So the LCM of 24 and 36 is 72

But, if you have big/nasty numbers

• This is takes ages

• Easy to make a mistake

LCM – Using Factor Trees

1. First write each number as a product of its primes

2. Find the Highest Common Factor by identifying the primes which appear in both numbers

3. Find the Lowest Common Multiple by multiplying the Highest Common Factor by all the factors that are leftover.

Find the LCM of 45 and 72

HELP!!

1. Product of Primes

• 45 • 72

45

33

95

72

2 36

182

3

2 9

33 x 3 x 5 = 4532 x 5 = 45

2 x 2 x 2 x 3 x 3 = 7223 x 32 = 72

2. Highest Common Factor

• 45 • 72

45

33

95

72

2 36

182

3

2 9

3HCF = 3 x 3 = 9

3. LCM = HCF x Leftovers

• 45 • 7272

2 36

182

3

2 9

3

HCF = 3 x 3 = 9

45

33

95

Leftovers = 5 x 23 = 40

LCM = 9 x 40 = 360

Find the HCF and then LCM of the following:

1. 18 and 30

2. 27 and 36

3. 14 and 35

4. 15 and 55

5. 24 and 56

6. 35 and 42

7. 56 and 100

8. 108 and 126

= 90= 108= 70= 165= 168= 210= 1400= 756