Least Common Multiple  of 31 and 38 is 1178

How to find the Least Common Multiple of 31 and 38?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 31 and 38.

Follow the steps below, and let's calculate the LCM of 31 and 38.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 31 and 38:

Prime factors of 31

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

31 = 311

Prime factors of 38

The prime factors of 38 are 2 and 19. Prime factorization of 38 in exponential form is:

38 = 21x191


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

311, 21, 191


Step 3: Multiply these values together:

311x21x191=1178


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 31 and 38.

The Least Common Multiple of 31 and 38 is 1178.


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

Multiples of 38:

38, 76, 114, 152, 190, 228, 266, 304, 342, 380, 418, 456, 494, 532, 570, 608, 646, 684, 722, 760, 798, 836, 874, 912, 950, 988, 1026, 1064, 1102, 1140, 1178, 1216, 1254, 1292


Therefore,

LCM(31, 38) = 1178