How to Find the LCM of Numbers

The least common multiple (LCM) of two or more numbers is the smallest number into which those numbers can all divide evenly, meaning without a remainder. Being able to find the least common multiple of a set of numbers is an important math skill to learn because it will be a skill that you will use over and over again throughout your math career to help you tackle other math problems.

Things You'll Need

• Paper
• Pencil
• Calculator (optional)

Instructions

1. Take your paper and pencil and write each of your numbers at the top of the page, leaving some space between each so you can list numbers below them.

2. Write on the next line the product of the each number and 2 in the correct column, then on the next line the product of each number and 3, and so on down the paper through at least 10 to begin with. For example, if you were working with the numbers 9 and 12 then you would list 18, 27, 36 and so on beneath your 9 all the way to 90. Below the 12 you would write 24, 36, 48 and so on all the way to 120.

3. Examine the lists of numbers that you have to determine if a number appears in all of your lists of numbers. If a number does appear in all of your lists then that number is the least common multiple. Remember you are looking for the smallest number that appears in all the lists, in case there is more than one number that appears in all the lists. So, for our example from above we would notice pretty quickly that 36 appears on both of our lists and there are no numbers smaller than 36 that appear on both lists, so 36 is the least common multiple.

4. Continue multiplying each of your numbers past 10 if you haven't yet reached a number that appears on all of your lists until you do reach a number that appears on all of your lists.

5. Check your answer from above using the shortcut method to find the LCM, but if you are just beginning to study the concept of LCMs, then you should use the method above to find your answer to help reinforce the meaning of "least common multiple." The shortcut method for finding the LCM is to find the greatest common factor of your numbers, then multiply all your numbers together, and divide the product by the greatest common factor.