Definition:

Least Common Multiple (LCM) – Is the smallest multiple that two or more numbers have in common.

Example 1: Find the LCM of 5 and 7 by listing the multiples.

Multiples of 5: 5, 10, 15, 20, 25, 30, 35

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

35 is the least common multiple of 5 and 7 because it is the smallest number that both numbers go into.

Method 1: Finding The LCM by Listing the Multiples

Strategy:1.) List the multiples of each number.2.) Identify the smallest common multiple that both numbers have in common.

Example 1: Find the Least Common Multiple of 10 and 12.

Strategy:1.) Go through the prime numbers starting from 2.2.) If a number is divisible by the prime number, then write the quotient. If it is not, carry the number down. If you can use the same prime number twice, then do so.

3.) Work through the process until each number has a 1 in its column (one and you’re DONE).4.) Multiply the prime numbers in your table together to get the LCM.

Method 2: Finding The LCM by Using a Table

2 • 2 • 3 • 5 = 60 Multiply the prime numbers. 60 is the LCM of 12 and 10.

Prime Numbers 2 10 12 2 5 6

3 5 3

5 5 1 1

Example 2: Find the Least Common Multiple of 4, 5 and 9.

Method 2: Finding The LCM by Using a Table

2 • 2 • 3 • 3 • 5 = 180Multiply the prime numbers. 180 is the LCM of 4, 5 and 9.

Prime Numbers 2 4 5 9 2 2 5 9

3 1 5 9

3 5 3

5 5 1 1

Strategy:1.) Go through the prime numbers starting from 2.2.) If a number is divisible by the prime number, then write the quotient. If it is not, carry the number down. If you can use the same prime number twice, then do so.

3.) Work through the process until each number has a 1 in its column (one and you’re DONE).4.) Multiply the prime numbers in your table together to get the LCM.

Find the least common multiple of the following sets of numbers by using a table.

1.) 5 and 16 2.) 5, 8 and 10 3.) 12, 15 and 20

Danna has painting class every two weeks. Nathaly has a pottery class every five weeks. Danna and Nathaly met at the art studio for class this week. How many weeks will it be until they see each other again at the art studio?

Real-Life Application