Least Common Multiple of 309 and 314

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 309 and 314 the smallest integer that is 97026 that is divisible by both numbers.

Least Common Multiple (LCM) of 309 and 314 is 97026.

LCM(309,314) = 97026

LCM of 309 and 314

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

LCM of:
and

Least Common Multiple of 309 and 314

LCM of 309 and 314 is 97026

Least common multiple can be found by multiplying the highest exponent prime factors of 309 and 314. First we will calculate the prime factors of 309 and 314.

Prime Factorization of 309


3 309
103 103
1

Prime factors of 309 are 3,103. Prime factorization of 309 in exponential form is:

309 = 31×1031

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

Now multiplying the highest exponent prime factors to calculate the LCM of 309 and 314.

LCM(309,314) = 21×31×1031×1571
LCM(309,314) = 97026

Factors of 309

List of positive integer factors of 309 that divides 309 without a remainder.

1, 3, 103, 309

Factors of 314

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

1, 2, 157, 314

Least Common Multiple of 309 and 314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 309 and 314, than apply into the LCM equation.

GCF(309,314) = 1
LCM(309,314) = ( 309 × 314) / 1
LCM(309,314) = 97026 / 1
LCM(309,314) = 97026

Properties of LCM 309 and 314

(i) The LCM of 314 and 309 is associative

LCM of 309 and 314 = LCM of 314 and 309

Related Least Common Multiples of 309

Related Least Common Multiples of 314

Frequently Asked Questions on LCM of 309 and 314

1. What is the LCM of 309 and 314?

Answer: LCM of 309 and 314 is 97026.

2. What are the Factors of 309?

Answer: Factors of 309 are 1, 3, 103, 309. There are 4 integers that are factors of 309. The greatest factor of 309 is 309.

3. 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.

4. How to Find the LCM of 309 and 314?

Answer:

Least Common Multiple of 309 and 314 = 97026

Step 1: Find the prime factorization of 309

309 = 3 x 103

Step 2: Find the prime factorization of 314

314 = 2 x 157

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

LCM = 97026 = 2 x 3 x 103 x 157

Step 4: Therefore, the least common multiple of 309 and 314 is 97026.