 ## How to find the Least Common Multiple of 34 and 45?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 34 and 45.

Follow the steps below, and let's calculate the LCM of 34 and 45.

### Method 1 - Prime factorization

#### Step 1: Create a list of all the prime factors of the numbers 34 and 45:

##### Prime factors of 34

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

34 = 21x171

##### Prime factors of 45

The prime factors of 45 are 3, 3 and 5. Prime factorization of 45 in exponential form is:

45 = 32x51

21, 171, 32, 51

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

21x171x32x51=1530

#### Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 34 and 45.

The Least Common Multiple of 34 and 45 is 1530.

### 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, 816, 850, 884, 918, 952, 986, 1020, 1054, 1088, 1122, 1156, 1190, 1224, 1258, 1292, 1326, 1360, 1394, 1428, 1462, 1496, 1530, 1564, 1598, 1632

#### Multiples of 45:

45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675, 720, 765, 810, 855, 900, 945, 990, 1035, 1080, 1125, 1170, 1215, 1260, 1305, 1350, 1395, 1440, 1485, 1530, 1575, 1620, 1665

#### Therefore,

LCM(34, 45) = 1530