Math Chapter: Greatest Common Factor and Least Common Multiple

Common Factors

Greatest Common Factor (GCF)

• The GCF is the largest number that divides two or more numbers exactly without leaving a remainder.
• It is also known as the Highest Common Factor (HCF).
• To find the GCF, list the factors of each number and identify the common factors.
• The GCF is the largest of these common factors.

Example: Find the GCF of 12 and 15. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 15: 1, 3, 5, 15 Common factors: 1, 3 GCF: 3

Least Common Factor (LCF)

• Note: There is no such thing as the Least Common Factor (LCF). The term "Least Common Factor" is often confused with the Least Common Multiple (LCM).
• The LCM is the smallest number that is a multiple of two or more numbers.
• To find the LCM, list the multiples of each number and identify the first common multiple.
• The LCM is the smallest of these common multiples.

Example: Find the LCM of 4 and 6. Multiples of 4: 4, 8, 12, 16, 20, ... Multiples of 6: 6, 12, 18, 24, 30, ... First common multiple: 12 LCM: 12

Greatest Common Factor (GCF)

• The GCF is the largest number that divides two or more numbers exactly without leaving a remainder.
• It is also known as the Highest Common Factor (HCF).
• To find the GCF, list the factors of each number and identify the common factors.
• The GCF is the largest of these common factors.

Finding the GCF

• List the factors of each number.
• Identify the common factors.
• The largest of these common factors is the GCF.

Example of Finding the GCF

• Find the GCF of 12 and 15.
• Factors of 12: 1, 2, 3, 4, 6, 12.
• Factors of 15: 1, 3, 5, 15.
• Common factors: 1, 3.
• GCF: 3.

Least Common Factor (LCF)

• There is no such thing as the Least Common Factor (LCF).
• The term "Least Common Factor" is often confused with the Least Common Multiple (LCM).

Least Common Multiple (LCM)

• The LCM is the smallest number that is a multiple of two or more numbers.
• To find the LCM, list the multiples of each number and identify the first common multiple.
• The LCM is the smallest of these common multiples.

Finding the LCM

• List the multiples of each number.
• Identify the first common multiple.
• The smallest of these common multiples is the LCM.

Example of Finding the LCM

• Find the LCM of 4 and 6.
• Multiples of 4: 4, 8, 12, 16, 20,...
• Multiples of 6: 6, 12, 18, 24, 30,...
• First common multiple: 12.
• LCM: 12.