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Math Foundations

You will find the least common multiple of two or more numbers.

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After completing this tutorial, you will be able to complete the following:

- Explain the concept of least common multiple.
- Determine the least common multiple of two numbers.
- Determine the least common multiple of three or more numbers.

It is important for students to understand the value of finding the least common multiple (LCM) for numbers because they will use the procedure regularly when adding and subtracting fractions with unlike denominators.

The following key vocabulary terms will be used throughout this Activity Object. Be sure that students are unable to define and provide an example for each one before presenting the Activity Object.

Composite number - A number which has more than two factors. All composite numbers are the product of prime numbers. Composite numbers can be broken down into the prime numbers using prime factorization.

Example:

24 is a composite number.

Its factors are 1, 2, 3, 4, 6, 8, 12, and 24.

Its prime factorization is ....

24 = 2 ´ 2 ´ 2 ´ 3

= 23 ´ 3

Factor - a factor of a number will divide that number exactly, without any remainder

Example:

2 is a factor of 16 because 2 goes into 16 exactly 8 times, with no remainder.

Least common multiple (LCM) - The smallest multiple two or more numbers have in common. The LCM can be determined by listing the multiples in order for each number or by using prime factorization.

Example:

Find the LCM of 4, 5 and 6.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

4, 5, 6 have a common multiple of 60. It is the smallest multiple all three numbers have in common. The LCM is 60.

OR

4 = 2 ´ 2

= 22

5 is already a prime number. It cannot be broken down into smaller prime numbers.

6 = 2 ´ 3

The product of the highest power of each prime factor of the numbers is the LCM. In this example 22, 3, and 5 are the highest power of each prime factor. Therefore the LCM = 22 ´ 3 ´ 5 = 60.

Multiple - a multiple of a number is the product of that number and another number

Example:

16 is a multiple of 2 because 2 times 8 is 16.

(Hint: A multiple is the opposite of a factor.)

Prime factorization - a process of breaking down a composite number into the product of prime numbers

Example:

12 = 2 ´ 2 ´ 3

= 22 ´ 3

2 ´ 2 is written in a simplified format using an exponent.

22 is 2 to the second power or 2 ´ 2.

When determining LCM, use the product of all of the highest power prime numbers.

Prime numbers - a number which has a factor of one and itself (1 is neither prime nor composite)

Approximate Time | 25 Minutes |

Pre-requisite Concepts | Students should be familiar with factors, multiples, prime factorization, and prime numbers. |

Course | Math Foundations |

Type of Tutorial | Concept Development |

Key Vocabulary | multiples, prime factorization, least common multiple |