Least Common Multiple of 10309 and 10314

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10309 and 10314 the smallest integer that is 106327026 that is divisible by both numbers.

Least Common Multiple (LCM) of 10309 and 10314 is 106327026.

LCM(10309,10314) = 106327026

LCM of 10309 and 10314

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

LCM of:
and

Least Common Multiple of 10309 and 10314

LCM of 10309 and 10314 is 106327026

Least common multiple can be found by multiplying the highest exponent prime factors of 10309 and 10314. First we will calculate the prime factors of 10309 and 10314.

Prime Factorization of 10309


13 10309
13 793
61 61
1

Prime factors of 10309 are 13,61. Prime factorization of 10309 in exponential form is:

10309 = 132×611

Prime Factorization of 10314


2 10314
3 5157
3 1719
3 573
191 191
1

Prime factors of 10314 are 2, 3,191. Prime factorization of 10314 in exponential form is:

10314 = 21×33×1911

Now multiplying the highest exponent prime factors to calculate the LCM of 10309 and 10314.

LCM(10309,10314) = 21×33×132×611×1911
LCM(10309,10314) = 106327026

Factors of 10309

List of positive integer factors of 10309 that divides 10309 without a remainder.

1, 13, 61, 169, 793, 10309

Factors of 10314

List of positive integer factors of 10314 that divides 10314 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 191, 382, 573, 1146, 1719, 3438, 5157, 10314

Least Common Multiple of 10309 and 10314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10309 and 10314, than apply into the LCM equation.

GCF(10309,10314) = 1
LCM(10309,10314) = ( 10309 × 10314) / 1
LCM(10309,10314) = 106327026 / 1
LCM(10309,10314) = 106327026

Properties of LCM 10309 and 10314

(i) The LCM of 10314 and 10309 is associative

LCM of 10309 and 10314 = LCM of 10314 and 10309

Related Least Common Multiples of 10309

Related Least Common Multiples of 10314

Frequently Asked Questions on LCM of 10309 and 10314

1. What is the LCM of 10309 and 10314?

Answer: LCM of 10309 and 10314 is 106327026.

2. What are the Factors of 10309?

Answer: Factors of 10309 are 1, 13, 61, 169, 793, 10309. There are 6 integers that are factors of 10309. The greatest factor of 10309 is 10309.

3. What are the Factors of 10314?

Answer: Factors of 10314 are 1, 2, 3, 6, 9, 18, 27, 54, 191, 382, 573, 1146, 1719, 3438, 5157, 10314. There are 16 integers that are factors of 10314. The greatest factor of 10314 is 10314.

4. How to Find the LCM of 10309 and 10314?

Answer:

Least Common Multiple of 10309 and 10314 = 106327026

Step 1: Find the prime factorization of 10309

10309 = 13 x 13 x 61

Step 2: Find the prime factorization of 10314

10314 = 2 x 3 x 3 x 3 x 191

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

LCM = 106327026 = 2 x 3 x 3 x 3 x 13 x 13 x 61 x 191

Step 4: Therefore, the least common multiple of 10309 and 10314 is 106327026.