## How to find the Least Common Multiple of 34 and 40?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 34 and 40.

Follow the steps below, and let's calculate the LCM of 34 and 40.

### Method 1 - Prime factorization

#### Step 1: Create a list of all the prime factors of the numbers 34 and 40:

##### Prime factors of 34

The prime factors of **34** are **2 and 17**.
Prime factorization of **34** in exponential form is:

**34** = 2^{1}x17^{1}

##### Prime factors of 40

The prime factors of **40** are **2, 2, 2 and 5**.
Prime factorization of **40** in exponential form is:

**40** = 2^{3}x5^{1}

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

2^{3}, 17^{1}, 5^{1}

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

2^{3}x17^{1}x5^{1}=**680**

#### Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 34 and 40.

The Least Common Multiple of **34 and 40** is **680**.

### 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 **34**:

34, 68, 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, 612, 646, 680, 714, 748, 782

#### Multiples of **40**:

40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800

#### Therefore,

LCM(34, 40) = **680**