Least Common Multiple

Least Common Multiple (LCM)
The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is a multiple of all of those numbers.

The following diagrams show how to find the Least Common Multiple (LCM): by Listing out the Multiple, by using Prime Factorization, by using Repeated Division. Scroll down the page for examples and solutions.

 

Factors & Multiples Worksheets
Practice your Factors & Multiples skills with the following worksheets:
Printable & Online Factors & Multiples Worksheets

Methods to Find LCM

Method 1: Listing Multiples

1. List multiples of each number.
2. Identify the smallest shared multiple.

Method 2: Prime Factorization

1. Factorize each number into primes. (You can use a factor tree)
2. Take the highest power of each prime.
3. Multiply them.

Method 3: Repeated Division (Ladder method

1. Write the numbers side by side.
2. Divide all numbers by the smallest prime factor (2, 3, 5, etc.) that divides at least one of them.
3. Repeat until no common prime factors remain.
4. Multiply all the divisors and remaining numbers to get the LCM.

Method 4: Using the GCF (Greatest Common Factor)
Formula: LCM(a, b) = (a × b) ÷ GCF(a, b).

Example:
Find the LCM of 2, 3 and 6.

Solution:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, …
Multiples of 3: 3, 6, 9, 12, 15, 18, …
Multiples of 6: 6, 12, 18, …

The common multiples are 6, 12, 18, …

The smallest among them is 6.

Therefore, the Least Common Multiple (LCM) is 6.

Repetitive Division

Using the lists to find the LCM can be slow and tedious. A faster way is to use repetitive division to find the least common multiple.

Divide the numbers by prime numbers. If a number cannot be divided it is copied down to the next step of division.

For example, to find the LCM of 3, 6 and 9, we divide them by any factor of the numbers in the following manner:

 

Least Common Multiple (LCM)
Find the LCM by listing the multiples of each number and find the smallest one that is common.
Another method is to use prime factorization.

Example:
What is the least common multiple (lcm) of 15, 6, and 10?

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How to obtain the least common multiple using the repetitive division method?

Example:
Finding the LCM of 3 or more numbers

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