Least Common Multiple  of 31 and 42 is 1302

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


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

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