1.3 Highest Common Factor and Lowest Common Multiple

Highest Common Factor (HCF)

• It is the largest number that divides two or more numbers exactly

• Used to simplify fractions and solve problems involving sharing or grouping

• Found by:

  • Listing all factors of each number

  • Identifying the common factors

  • Choosing the largest one

• Example:

  • Factors of 12: 1, 2, 3, 4, 6, 12

  • Factors of 18: 1, 2, 3, 6, 9, 18

  • HCF = 6

Lowest Common Multiple (LCM)

• It is the smallest number that is a multiple of two or more numbers

• Used to solve problems involving synchronization, repetition, or common timing

• Found by:

  • Listing the multiples of each number

  • Identifying the common multiples

  • Choosing the smallest one

• Example:

  • Multiples of 4: 4, 8, 12, 16, 20, 24...

  • Multiples of 6: 6, 12, 18, 24, 30...

  • LCM = 12

Expressing a number as a product of it’s prime factors