Least Common Multiple of 314 and 320

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 320 the smallest integer that is 50240 that is divisible by both numbers.

Least Common Multiple (LCM) of 314 and 320 is 50240.

LCM(314,320) = 50240

LCM of 314 and 320

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

LCM of:
and

Least Common Multiple of 314 and 320

LCM of 314 and 320 is 50240

Least common multiple can be found by multiplying the highest exponent prime factors of 314 and 320. First we will calculate the prime factors of 314 and 320.

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 320


2 320
2 160
2 80
2 40
2 20
2 10
5 5
1

Prime factors of 320 are 2,5. Prime factorization of 320 in exponential form is:

320 = 26×51

Now multiplying the highest exponent prime factors to calculate the LCM of 314 and 320.

LCM(314,320) = 26×51×1571
LCM(314,320) = 50240

Factors of 314

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

1, 2, 157, 314

Factors of 320

List of positive integer factors of 320 that divides 320 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320

Least Common Multiple of 314 and 320 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 320, than apply into the LCM equation.

GCF(314,320) = 2
LCM(314,320) = ( 314 × 320) / 2
LCM(314,320) = 100480 / 2
LCM(314,320) = 50240

Properties of LCM 314 and 320

(i) The LCM of 320 and 314 is associative

LCM of 314 and 320 = LCM of 320 and 314

Related Least Common Multiples of 314

Related Least Common Multiples of 320

Frequently Asked Questions on LCM of 314 and 320

1. What is the LCM of 314 and 320?

Answer: LCM of 314 and 320 is 50240.

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 320?

Answer: Factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320. There are 14 integers that are factors of 320. The greatest factor of 320 is 320.

4. How to Find the LCM of 314 and 320?

Answer:

Least Common Multiple of 314 and 320 = 50240

Step 1: Find the prime factorization of 314

314 = 2 x 157

Step 2: Find the prime factorization of 320

320 = 2 x 2 x 2 x 2 x 2 x 2 x 5

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

LCM = 50240 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 157

Step 4: Therefore, the least common multiple of 314 and 320 is 50240.