 ## How to find the Least Common Multiple of 31 and 42?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 31 and 42.

Follow the steps below, and let's calculate the LCM of 31 and 42.

### Method 1 - Prime factorization

#### Step 1: Create a list of all the prime factors of the numbers 31 and 42:

##### Prime factors of 31

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

31 = 311

##### Prime factors of 42

The prime factors of 42 are 2, 3 and 7. Prime factorization of 42 in exponential form is:

42 = 21x31x71

311, 21, 31, 71

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

311x21x31x71=1302

#### Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 31 and 42.

The Least Common Multiple of 31 and 42 is 1302.

### 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 31:

31, 62, 93, 124, 155, 186, 217, 248, 279, 310, 341, 372, 403, 434, 465, 496, 527, 558, 589, 620, 651, 682, 713, 744, 775, 806, 837, 868, 899, 930, 961, 992, 1023, 1054, 1085, 1116, 1147, 1178, 1209, 1240, 1271, 1302, 1333, 1364, 1395

#### Multiples of 42:

42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, 546, 588, 630, 672, 714, 756, 798, 840, 882, 924, 966, 1008, 1050, 1092, 1134, 1176, 1218, 1260, 1302, 1344, 1386, 1428

#### Therefore,

LCM(31, 42) = 1302