Least Common Multiple of 314 and 321

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 314 and 321 the smallest integer that is 100794 that is divisible by both numbers.

Least Common Multiple (LCM) of 314 and 321 is 100794.

LCM(314,321) = 100794

LCM of 314 and 321

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

LCM of:
and

Least Common Multiple of 314 and 321

LCM of 314 and 321 is 100794

Least common multiple can be found by multiplying the highest exponent prime factors of 314 and 321. First we will calculate the prime factors of 314 and 321.

Prime Factorization of 314


2 314
157 157
1

Prime factors of 314 are 2,157. Prime factorization of 314 in exponential form is:

314 = 21×1571

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

Now multiplying the highest exponent prime factors to calculate the LCM of 314 and 321.

LCM(314,321) = 21×31×1071×1571
LCM(314,321) = 100794

Factors of 314

List of positive integer factors of 314 that divides 314 without a remainder.

1, 2, 157, 314

Factors of 321

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

1, 3, 107, 321

Least Common Multiple of 314 and 321 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 314 and 321, than apply into the LCM equation.

GCF(314,321) = 1
LCM(314,321) = ( 314 × 321) / 1
LCM(314,321) = 100794 / 1
LCM(314,321) = 100794

Properties of LCM 314 and 321

(i) The LCM of 321 and 314 is associative

LCM of 314 and 321 = LCM of 321 and 314

Related Least Common Multiples of 314

Related Least Common Multiples of 321

Frequently Asked Questions on LCM of 314 and 321

1. What is the LCM of 314 and 321?

Answer: LCM of 314 and 321 is 100794.

2. What are the Factors of 314?

Answer: Factors of 314 are 1, 2, 157, 314. There are 4 integers that are factors of 314. The greatest factor of 314 is 314.

3. 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.

4. How to Find the LCM of 314 and 321?

Answer:

Least Common Multiple of 314 and 321 = 100794

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 321

321 = 3 x 107

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

LCM = 100794 = 2 x 3 x 107 x 157

Step 4: Therefore, the least common multiple of 314 and 321 is 100794.