Least Common Multiple  of 31 and 39 is 1209

How to find the Least Common Multiple of 31 and 39?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 31 and 39.

Follow the steps below, and let's calculate the LCM of 31 and 39.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 31 and 39:

Prime factors of 31

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

31 = 311

Prime factors of 39

The prime factors of 39 are 3 and 13. Prime factorization of 39 in exponential form is:

39 = 31x131


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

311, 31, 131


Step 3: Multiply these values together:

311x31x131=1209


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 31 and 39.

The Least Common Multiple of 31 and 39 is 1209.


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

Multiples of 39:

39, 78, 117, 156, 195, 234, 273, 312, 351, 390, 429, 468, 507, 546, 585, 624, 663, 702, 741, 780, 819, 858, 897, 936, 975, 1014, 1053, 1092, 1131, 1170, 1209, 1248, 1287, 1326


Therefore,

LCM(31, 39) = 1209