1. Least Common Multiple

2. (1) MANUAL METHOD Example: find the least common multiple of 10 and 15
To find the Least Common Multiple of two numbers:
Write the multiples of each number
Select the common ones
Choose the least
Example: find the least common multiple of 10 and 15
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, …..
Multiples of 15: 15, 30, 45, 60, 75, 90…..
We take the least one, so LCM(10,15) = 30

3. LCM(4, 12) = 12 LCM(4, 12,8) = 24 Exercise 1: find the LCM (4, 12)
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40….
Multiples of 12: 12, 24, 36, 48, 60, 72,……
LCM(4, 12) = 12
Exercise 2: find the LCM (4, 12, 8)
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40….
Multiples of 12: 12, 24, 36, 48, 60, 72,……
Multiples of 8: 8, 16, 24, 32, 40,48, 56 ….
LCM(4, 12,8) = 24

4. = 24 (2) PRIME FACTORIZATION METHOD LCM(4, 24) =
To find the Least Common Multiple of two numbers:
Write the PRIME FACTORIZATION of each number
Select all the factors with the BIGGEST exponent
Multiply them
Example: find the least common multiple of 4 and 24
Write the prime factorization of 4 and 12:
LCM(4, 24) =
= 24

5. Exercise 3: find the LCM (20, 30)

6. Exercise 4: find the LCM (20, 30, 45)
= 180

7. Exercise 5