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Multiples and factors - AQAHighest common factor and lowest common multiple

Prime numbers, factors and multiples are essential building blocks for a lot of number work. Knowledge of how to use these numbers will improve arithmetic and make calculations more efficient.

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Highest common factor and lowest common multiple

Highest common factor

A common factor is a 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.

Lowest common multiple

A common multiple is a number that is a shared 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.