LCM and GCF

Today we will be learning how to find the LCM of two numbers

For example 2 and 3. 

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 ….
The LCM of 2 and 3 is 6

Example:

The least common multiple is defined as the smallest multiple that two or more numbers have in common..

​What is LCM?

LCM

​On way to find the LCM is to skip count.

12, 24, 36, 48, 60, 72
16, 32, 48, 64, 80, 96
The LCM of 12 and 16 is 48

Multiple Choice

Find the LCM of 6 and 9

• 12

• 18

• 27

• 54

Prime Factorization Method

The prime factorization method involves finding the prime factors of the given numbers and identifying the least common multiple (LCM). For example, pair the common multiples shown to find the least common multiple of 12 and 16 using the prime factorization. List them along with the remaining multiples.

The LCM for 12 and 16 is
LCM = 2 × 2 × 2 × 2 × 3 = 48

​

You only use the same numbers once.

Multiple Choice

Find the LCM for 3 and 12

• 24

• 36

• 12

• 18

Finding GCF

What is GCF?

In simple words, GCF is the largest number that divides the given set of integers evenly, without leaving any remainder.

What is a factor?

A factor is a number that divides another number evenly, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product. A number is always a factor of itself. 1 is a factor of all numbers. 

Example:

Example: The factors 20 are 1, 2, 4, 5, 10 and 20. 

Open Ended

What are the factors of 10?

Common Factors

As the name implies, a common factor of two or more numbers is a factor shared between the given set of numbers. In other words, it is a number that can evenly divide a set of two or more numbers.

Find common factors of 24 and 30. 

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Common factors of 24 and 30: 1, 2, 3, 6

Fill in the Blanks

Find the GCF of 20 and 25. (hint there is only one besides 1)