Unit 1.4: Least Common Multiple and Greatest Common Factor
Least Common Multiple (LCM)
The lowest number that is divisible by a set of numbers. It is found by listing all of the prime factors of each number and then multiplying them together
Least Common Multiple
Find the LCM of 16 and 20
Start by listing all the prime factors of each number
16: 20:
16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 20 = 2 ⋅ 2 ⋅ 5
Because 16 and 20 share some common numbers, we only need to use the repeats once
It becomes 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 = 80
The LCM {16, 20} = 80
Greatest Common Factor (GCF)
The highest number that a set of numbers is divisible by
Greatest Common Factor
Find the GCF of 30 and 65
Start by listing all the factors of the two numbers
30: (1, 30) (2, 15) (3, 10) (5, 6)
65: (1, 65) (5, 13)
Look for the highest number both have in common
in this case its 5 so the GCF {30, 65} is 5