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basic explanation:

The least common multiple is the smallest common multiple of one or numbers. Whenever there is only one number you are finding the least common multiple for, the least common multiple is always that number. For example, 23 is the least common multiple of 23 because that is the smallest common multiple. The least common multiple is often called the LCM for short. For futher details regarding how the least common multiple of numbers, please refer to the in-depth explanation.

in-depth explanation:

Multiples of numbers are found by staring to multiply the number by one, then multiplying the number by two, then three, and so on. For example, if you had to find the multiples of 5, the first multiple would be 5 (5 × 1 = 5), then 10 (5 × 2 = 10), and so on. There are an infinite number of multiples for every number, but to find the lowest common multiple, you only have to continue finding multiples until every number you are finding multiples for has one multiple in common with each other. These are known as common multiples. The least common multiple of two or more numbers is the smallest common multiple. This will always be the first common multiple found, so there is no need to continue finding multiples once you have found a common multiple (if you used the way described to find multiples).

LCM practice problems:

To fully understand this concept, it is important to utilize your knowledge through problems. Rather than creating your own, you can simply use some of the ones from our collection of LCM problems below. They are categorized into three different categories: easy, medium, and hard. It is recommended you begin with the easy problems and work your way up from there. If you are having difficulties solving any of the problems, you may use our LCM calculator which will calculate the answer and provide steps on how the problem was solved. You may also use the calculator to check you got the correct answer.

easy:

1.) The LCM of 12 and 3 is ?.

2.) The LCM of 4 and 8 is ?.

3.) The LCM of 30 and 5 is ?.

4.) The LCM of 9 and 27 is ?.

5.) The LCM of 1, 4, and 2 is ?.

6.) The LCM of 18 and 3 is ?.

7.) The LCM of 24 and 6 is ?.

8.) The LCM of 34 and 2 is ?.

9.) The LCM of 22 and 4 is ?.

10.) The LCM of 70 and 5 is ?.

medium:

1.) The LCM of 50 and 20 is ?

2.) The LCM of 64 and 12 is ?

3.) The LCM of 70, 13, and 4 is ?

4.) The LCM of 2, 80, and 33 is ?

5.) The LCM of 34, 12, and 8 is ?

6.) The LCM of 53 and 23 is ?.

7.) The LCM of 13, 40, and 9 is ?.

8.) The LCM of 64, 12, and 5 is ?.

9.) The LCM of 12, 50, and 4 is ?.

10.) The LCM of 43, 80, and 23 is ?.

hard:

1.) The LCM of 802, 13, and 9 is ?.

2.) The LCM of 900, 33, and 23 is ?.

3.) The LCM of 2, 8, 64, 4, and 32 is ?.

4.) The LCM of 12, 80, and 324 is ?.

5.) The LCM of 124 and 908 is ?.

6.) The LCM of 134, 345, and 923 is ?.

7.) The LCM of 122, 544, and 754 is ?.

8.) The LCM of 357, 122, and 234 is ?.

9.) The LCM of 2,123 and 4,590 is ?.

10.) The LCM of 10,344, 5,123, and 2,333 is ?.