## How to find the Least Common Multiple of 18 and 31?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 18 and 31.

Follow the steps below, and let's calculate the LCM of 18 and 31.

### Method 1 - Prime factorization

#### Step 1: Create a list of all the prime factors of the numbers 18 and 31:

##### Prime factors of 18

The prime factors of **18** are **2, 3 and 3**.
Prime factorization of **18** in exponential form is:

**18** = 2^{1}x3^{2}

##### Prime factors of 31

The prime factors of **31** are **31**.
Prime factorization of **31** in exponential form is:

**31** = 31^{1}

#### Step 2: Identify the highest power of each prime number from the above boxes:

2^{1}, 3^{2}, 31^{1}

#### Step 3: Multiply these values together:

2^{1}x3^{2}x31^{1}=**558**

#### Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 18 and 31.

The Least Common Multiple of **18 and 31** is **558**.

### Method 2 - List of Multiples

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

#### Multiples of **18**:

18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360, 378, 396, 414, 432, 450, 468, 486, 504, 522, 540, 558, 576, 594, 612

#### Multiples of **31**:

31, 62, 93, 124, 155, 186, 217, 248, 279, 310, 341, 372, 403, 434, 465, 496, 527, 558, 589, 620, 651

#### Therefore,

LCM(18, 31) = **558**