Highest common factor and lowest common multiple

Highest common factor

A common factor is a factor that is shared by two or more numbers. For example, a common factor of 8 and 10 is 2, as 2 is a factor of 8, and 2 is also a factor of 10.

The highest common factor (HCF) is found by identifying all common factors of two numbers and selecting the largest one.

For example, 8 and 12 have common factors of 1, 2 and 4. The highest common factor is 4.

Question

Find the highest common factor of 9 and 21.

Start by listing the factors of 9 and 21:

  • factors of 9: 1, 3, 9
  • factors of 21: 1, 3, 7, 21

The common factors of 9 and 21 are 1 and 3, so the highest common factor of 9 and 21 is 3.

Lowest common multiple

A common multiple is a number that is a shared multiple of two or more numbers. For example, 24 is a common multiple of 8 and 12, as 24 is in the 8 times tables ( 8 \times 3 = 24) and 24 is in the 12 times tables ( 12 \times 2 = 24).

The lowest common multiple (LCM) is found by listing multiples of each number and circling any common multiples. The lowest one is the lowest common multiple.

Question

Find the lowest common multiple of 5 and 6.

List the multiples of 5 and 6:

  • multiples of 5: 5, 10, 15, 20, 25, 30, 35...
  • multiples of 6: 6, 12, 18, 24, 30...

The lowest common multiple of 5 and 6 is 30, as it is the first multiple found in both lists.