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Common multiples are multiples that two numbers have in common. These can be useful when working with fractions and ratios.

The lowest common multiple or least common multiple is the lowest multiple two numbers have in common.

There are two ways of finding the lowest common multiple of two numbers.

Method 1: Listing Multiples

The first way to find the lowest common multiple is to do what we did above: write out a list of the lowest multiples of each number, and look for the lowest multiple both numbers have in common.

Method 2: Factors

The other way to find the lowest common multiple is to list the prime factors for each number. Remove the prime factors both numbers have in common. Multiply one of the numbers by the remaining prime factors of the other number. The result will be the lowest common multiple.

You’ll get the same results no matter which number you work with:

Another Example

What if they have no prime factors in common?

As that last example illustrates, if two numbers have no prime factors in common, the lowest common multiple will be equal to the product of the two numbers.

Treat primes as prime factors

If one number is prime, you can treat it as its own prime factor.

Prime results

As you can see from the above, there are two scenarios if at least one number is prime:

  • If one number is prime, and the other number’s prime factors include that prime number, the lowest common multiple will be equal to the non-prime number.
  • If one number is prime, and the other number’s prime factors do not include that prime number, the lowest common multiple will be equal to the product of the two numbers.

(The second scenario also includes cases where both numbers are prime.)

Factors and Fractions

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Reducing Fractions to Lowest Terms

  • Reducing Fractions to Lowest Terms

TrendingHere are the facts and trivia that people are buzzing about.

Did Birds Evolve from Dinosaurs?

The Twelve Dancing Princesses

Current Events This Week: January 2023

African Americans by the Numbers

Andersen’s Fairy Tales: Contents

The Celtic Twilight: A Teller of Tales

TrendingHere are the facts and trivia that people are buzzing about.

Did Birds Evolve from Dinosaurs?

The Twelve Dancing Princesses

Current Events This Week: January 2023

African Americans by the Numbers

Andersen’s Fairy Tales: Contents

The Celtic Twilight: A Teller of Tales

  • Did Birds Evolve from Dinosaurs?
  • The Twelve Dancing Princesses
  • Current Events This Week: January 2023
  • African Americans by the Numbers
  • Andersen’s Fairy Tales: Contents
  • The Celtic Twilight: A Teller of Tales