Least Common Multiple of 309 and 316

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 316 the smallest integer that is 97644 that is divisible by both numbers.

Least Common Multiple (LCM) of 309 and 316 is 97644.

LCM(309,316) = 97644

LCM of 309 and 316

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

LCM of:
and

Least Common Multiple of 309 and 316

LCM of 309 and 316 is 97644

Least common multiple can be found by multiplying the highest exponent prime factors of 309 and 316. First we will calculate the prime factors of 309 and 316.

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 316


2 316
2 158
79 79
1

Prime factors of 316 are 2,79. Prime factorization of 316 in exponential form is:

316 = 22×791

Now multiplying the highest exponent prime factors to calculate the LCM of 309 and 316.

LCM(309,316) = 22×31×791×1031
LCM(309,316) = 97644

Factors of 309

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

1, 3, 103, 309

Factors of 316

List of positive integer factors of 316 that divides 316 without a remainder.

1, 2, 4, 79, 158, 316

Least Common Multiple of 309 and 316 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 316, than apply into the LCM equation.

GCF(309,316) = 1
LCM(309,316) = ( 309 × 316) / 1
LCM(309,316) = 97644 / 1
LCM(309,316) = 97644

Properties of LCM 309 and 316

(i) The LCM of 316 and 309 is associative

LCM of 309 and 316 = LCM of 316 and 309

Related Least Common Multiples of 309

Related Least Common Multiples of 316

Frequently Asked Questions on LCM of 309 and 316

1. What is the LCM of 309 and 316?

Answer: LCM of 309 and 316 is 97644.

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 316?

Answer: Factors of 316 are 1, 2, 4, 79, 158, 316. There are 6 integers that are factors of 316. The greatest factor of 316 is 316.

4. How to Find the LCM of 309 and 316?

Answer:

Least Common Multiple of 309 and 316 = 97644

Step 1: Find the prime factorization of 309

309 = 3 x 103

Step 2: Find the prime factorization of 316

316 = 2 x 2 x 79

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

LCM = 97644 = 2 x 2 x 3 x 79 x 103

Step 4: Therefore, the least common multiple of 309 and 316 is 97644.