Least Common Multiple  of 17 and 21 is 357

How to find the Least Common Multiple of 17 and 21?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 17 and 21.

Follow the steps below, and let's calculate the LCM of 17 and 21.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 17 and 21:

Prime factors of 17

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

17 = 171

Prime factors of 21

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

21 = 31x71


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

171, 31, 71


Step 3: Multiply these values together:

171x31x71=357


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 17 and 21.

The Least Common Multiple of 17 and 21 is 357.


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 17:

17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408

Multiples of 21:

21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420


Therefore,

LCM(17, 21) = 357