Least Common Multiple  of 21 and 34 is 714

How to find the Least Common Multiple of 21 and 34?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 21 and 34.

Follow the steps below, and let's calculate the LCM of 21 and 34.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 21 and 34:

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 34

The prime factors of 34 are 2 and 17. Prime factorization of 34 in exponential form is:

34 = 21x171


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

31, 71, 21, 171


Step 3: Multiply these values together:

31x71x21x171=714


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 21 and 34.

The Least Common Multiple of 21 and 34 is 714.


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, 735, 756, 777

Multiples of 34:

34, 68, 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, 612, 646, 680, 714, 748, 782, 816


Therefore,

LCM(21, 34) = 714