What is Least Common Multiple?

• It is the least or smallest common multiple of the given pairs of numbers.

• We also have the same methods in getting LCM just like in GCF.

• Listing Method, Factor Tree, and Continuous Division.

Example:

Get the least common factor of 4 and 7.

Listing Method

• List all the multiples of the pair of numbers.

• Identify the least common multiple of the given numbers.

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

• Multiples of 7: 7, 14, 21, 28, 35, 42, ...

Listing Method

• List all the multiples of the pair of numbers.

• Identify the least common multiple of the given numbers.

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

• Multiples of 7: 7, 14, 21, 28, 35, 42, ...

• LCM: 28

Example:

During the summer months, one ice cream cart visits Anne's village every 4 days and another ice cream cart visits her neighborhood every 5 days. If both carts visited today, when is the next time both carts will visit on the same day?

Example:

During the summer months, one ice cream cart visits May’s village every 4 days and another ice cream cart visits her neighborhood every 5 days. If both carts visited today, when is the next time both carts will visit on the same day?

4: 4, 8, 12, 16, 20, 24, 28, 32, ...

5: 5, 10, 15, 20, 25, 30, ...

Problems in getting the GCF may ask to:

• work out how many people we can invite 

• break up things into a smaller part;

• organize something into rows or groups

• equally distribute two or more sets of items into their largest grouping.

Problems in getting the LCM may inquire:

• about an event that will repeat

• when something will happen again at the same time; and

• how many items you will buy to have enough _?