What is the difference between LCM and HCF?

LCM stands for Lowest Common Multiple, and HCF stands for Highest Common Factor.

The key to telling the difference between these two things is knowing the difference between a multiple and a factor.

A multiple of an integer (whole number) is any integer that appears in its times table. For example, the multiples of 3 are 3, 6, 9, 12, and so on.

A factor of an integer is any integer that divides the integer with no remainder. For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

We use LCM and HCF to compare two (or more) integers.

The LCM of two integers is the smallest whole number that appears in both of their times tables, that is, the smallest integer that is a multiple of both numbers.

For example, the LCM of 4 and 5 is 20. To see this, look at the multiples (times table) of 4:

4, 8, 12, 16, 20, 24, 28, ...

and of 5:

5, 10, 15, 20, 25, ...

The LCM is 20 because this is the first number that appears in both lists.

The HCF of two integers is the largest whole number that divides both numbers without leaving a remainder.

For example, the HCF of 16 and 24 is 8. Again, we can look at both sets of factors and compare. The factors of 16 are:

1, 2, 4, 8, 16

and the factors of 24 are:

1, 2, 3, 4, 6, 8, 12, 24.

Although 2 and 4 are common factors (that is, they appear in both lists), we are looking for the highest common factor. The answer is 8.