Least Common Multiple of 314 and 322

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 322 the smallest integer that is 50554 that is divisible by both numbers.

Least Common Multiple (LCM) of 314 and 322 is 50554.

LCM(314,322) = 50554

LCM of 314 and 322

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

LCM of:
and

Least Common Multiple of 314 and 322

LCM of 314 and 322 is 50554

Least common multiple can be found by multiplying the highest exponent prime factors of 314 and 322. First we will calculate the prime factors of 314 and 322.

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 322


2 322
7 161
23 23
1

Prime factors of 322 are 2, 7,23. Prime factorization of 322 in exponential form is:

322 = 21×71×231

Now multiplying the highest exponent prime factors to calculate the LCM of 314 and 322.

LCM(314,322) = 21×71×231×1571
LCM(314,322) = 50554

Factors of 314

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

1, 2, 157, 314

Factors of 322

List of positive integer factors of 322 that divides 322 without a remainder.

1, 2, 7, 14, 23, 46, 161, 322

Least Common Multiple of 314 and 322 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 322, than apply into the LCM equation.

GCF(314,322) = 2
LCM(314,322) = ( 314 × 322) / 2
LCM(314,322) = 101108 / 2
LCM(314,322) = 50554

Properties of LCM 314 and 322

(i) The LCM of 322 and 314 is associative

LCM of 314 and 322 = LCM of 322 and 314

Related Least Common Multiples of 314

Related Least Common Multiples of 322

Frequently Asked Questions on LCM of 314 and 322

1. What is the LCM of 314 and 322?

Answer: LCM of 314 and 322 is 50554.

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 322?

Answer: Factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322. There are 8 integers that are factors of 322. The greatest factor of 322 is 322.

4. How to Find the LCM of 314 and 322?

Answer:

Least Common Multiple of 314 and 322 = 50554

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 322

322 = 2 x 7 x 23

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

LCM = 50554 = 2 x 7 x 23 x 157

Step 4: Therefore, the least common multiple of 314 and 322 is 50554.