Least Common Multiple  of 21 and 31 is 651

How to find the Least Common Multiple of 21 and 31?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 21 and 31.

Follow the steps below, and let's calculate the LCM of 21 and 31.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 21 and 31:

Prime factors of 21

The prime factors of 21 are 3 and 7. Prime factorization of 21 in exponential form is:

21 = 31x71

Prime factors of 31

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

31 = 311


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

31, 71, 311


Step 3: Multiply these values together:

31x71x311=651


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 21 and 31.

The Least Common Multiple of 21 and 31 is 651.


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 21:

21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714

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


Therefore,

LCM(21, 31) = 651