# Least Common Multiple Calculator

Welcome to our Least Common Multiple Calculator page.

This calculator will tell you the least common multiple between two or more numbers.

The calculator will also show you the step-by-step working out using two different methods.

There are also some worked examples to show you how it works.

### Least Common Multiple Calculator - The Multiples Method

#### Examples

Example 1) Find the least common multiple of 5 and 3.

The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, ...

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

So the least common multiple (the smallest number occurring in both lists) is 15.

Note that we really only needed to go up to the 3rd multiple of 5, or the 5th multiple of 3 to find our answer.

The Least Common Multiple is 15.

Example 2) Find the lowest common multiple of 5 and 11.

The multiples of 5 are: 5, 10, 15, 20 , 25, 30, 35, 40, 45, 50, 55, 60

The multiples of 11 are: 11, 22, 33, 44, 55, 66, ...

The smallest number on both lists is 55 (which is 5x11).

The Least Common Multiple is 55.

### Least Common Multiple Calculator - The Prime Factors Method

Example 1) Find the lowest common multiple of 14 and 20.

As a product of prime factors:

• 14 = 2 x 7
• 20 = 2 x 2 x 5 = 22 x 5

Next combine the factors and sort this list by order of number and exponent:

22, 2, 5, 7

Now remove any lower exponents of the same number from the list.

The factor 2 is repeated so we only need to use the highest exponent which is 22.

Our new list is:

22, 5, 7.

Now we multiple the factors of the list together.

This gives us: 22 x 5 x 7 = 2 x 2 x 5 x 7 = 140

The Least Common Multiple is 140.

Example 2) Find the least common multiple of 144 and 78.

As a product of prime factors:

• 144 = 2 x 2 x 2 x 2 x 3 x 3 = 24 x 32
• 78 = 2 x 3 x 13

Next combine the factors and sort this list by order of number and exponent:

24 x 2 x 32 x 3 x 13

Now remove any lower exponents of the same number from the list.

The factor 2 is repeated so we only need to use the highest exponent which is 24.

The factor 3 is repeated so we only need to use the highest exponent which is 32.

This gives us a final list of:

24, 32, 13.

Now we need to multiple the prime factors together to find the LCM.

This gives us: 24 x 32 x 13 = 2 x 2 x 2 x 2 x 3 x 3 x 13 = 1872

As you can probably see, this would take a while to work out using the multiples method!

The Least Common Multiple (LCM) is 1872.

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