Least Common Multiple of 321 and 324

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 321 and 324 the smallest integer that is 34668 that is divisible by both numbers.

Least Common Multiple (LCM) of 321 and 324 is 34668.

LCM(321,324) = 34668

LCM of 321 and 324

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 321 and 324

LCM of 321 and 324 is 34668

Least common multiple can be found by multiplying the highest exponent prime factors of 321 and 324. First we will calculate the prime factors of 321 and 324.

Prime Factorization of 321


3 321
107 107
1

Prime factors of 321 are 3,107. Prime factorization of 321 in exponential form is:

321 = 31×1071

Prime Factorization of 324


2 324
2 162
3 81
3 27
3 9
3 3
1

Prime factors of 324 are 2,3. Prime factorization of 324 in exponential form is:

324 = 22×34

Now multiplying the highest exponent prime factors to calculate the LCM of 321 and 324.

LCM(321,324) = 22×34×1071
LCM(321,324) = 34668

Factors of 321

List of positive integer factors of 321 that divides 321 without a remainder.

1, 3, 107, 321

Factors of 324

List of positive integer factors of 324 that divides 324 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324

Least Common Multiple of 321 and 324 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 321 and 324, than apply into the LCM equation.

GCF(321,324) = 3
LCM(321,324) = ( 321 × 324) / 3
LCM(321,324) = 104004 / 3
LCM(321,324) = 34668

Properties of LCM 321 and 324

(i) The LCM of 324 and 321 is associative

LCM of 321 and 324 = LCM of 324 and 321

Related Least Common Multiples of 321

Related Least Common Multiples of 324

Frequently Asked Questions on LCM of 321 and 324

1. What is the LCM of 321 and 324?

Answer: LCM of 321 and 324 is 34668.

2. What are the Factors of 321?

Answer: Factors of 321 are 1, 3, 107, 321. There are 4 integers that are factors of 321. The greatest factor of 321 is 321.

3. What are the Factors of 324?

Answer: Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324. There are 15 integers that are factors of 324. The greatest factor of 324 is 324.

4. How to Find the LCM of 321 and 324?

Answer:

Least Common Multiple of 321 and 324 = 34668

Step 1: Find the prime factorization of 321

321 = 3 x 107

Step 2: Find the prime factorization of 324

324 = 2 x 2 x 3 x 3 x 3 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 34668 = 2 x 2 x 3 x 3 x 3 x 3 x 107

Step 4: Therefore, the least common multiple of 321 and 324 is 34668.