Lowest Common Multiple

The lowest common multiple (LCM) of two numbers a and b is the lowest number that is a multiple of both of them.

You need it when adding or subtracting fractions, for example (see here)

One simple way to find it is to write down the first few multiples of a and b, looking for a number which is in both lists.

For example, to find the LCM of 8 and 12:

• multiples of 8 are 8, 16, 24, 32
• multiples of 12 are 12, 24, 36, 48

and the first number which appears in both lists is 24. However, for some pairs of numbers this can go on for a very long time.

There are a couple of special cases to watch out for.

if a goes into b then the LCM is b. For example, the LCM of 4 and 12 is 12.

if a and b have no common factor, so there is no number that goes into both of them except 1, then the LCM is a x b

If either number is prime then this will be the case, of course.

For example, the LCM of 5 and 23 is 5x23 = 115. This situation is worth looking out for as it is the one which will take a very long time if you are listing multiples of each number.

if you know the HCF (highest common factor) of a and b which is often possible to work out just by looking at the numbers, then -mathformula not MarkupType-
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