Least Common Multiple of 1309 and 1314

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1309 and 1314 the smallest integer that is 1720026 that is divisible by both numbers.

Least Common Multiple (LCM) of 1309 and 1314 is 1720026.

LCM(1309,1314) = 1720026

LCM of 1309 and 1314

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

LCM of:
and

Least Common Multiple of 1309 and 1314

LCM of 1309 and 1314 is 1720026

Least common multiple can be found by multiplying the highest exponent prime factors of 1309 and 1314. First we will calculate the prime factors of 1309 and 1314.

Prime Factorization of 1309


7 1309
11 187
17 17
1

Prime factors of 1309 are 7, 11,17. Prime factorization of 1309 in exponential form is:

1309 = 71×111×171

Prime Factorization of 1314


2 1314
3 657
3 219
73 73
1

Prime factors of 1314 are 2, 3,73. Prime factorization of 1314 in exponential form is:

1314 = 21×32×731

Now multiplying the highest exponent prime factors to calculate the LCM of 1309 and 1314.

LCM(1309,1314) = 21×32×71×111×171×731
LCM(1309,1314) = 1720026

Factors of 1309

List of positive integer factors of 1309 that divides 1309 without a remainder.

1, 7, 11, 17, 77, 119, 187, 1309

Factors of 1314

List of positive integer factors of 1314 that divides 1314 without a remainder.

1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314

Least Common Multiple of 1309 and 1314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1309 and 1314, than apply into the LCM equation.

GCF(1309,1314) = 1
LCM(1309,1314) = ( 1309 × 1314) / 1
LCM(1309,1314) = 1720026 / 1
LCM(1309,1314) = 1720026

Properties of LCM 1309 and 1314

(i) The LCM of 1314 and 1309 is associative

LCM of 1309 and 1314 = LCM of 1314 and 1309

Related Least Common Multiples of 1309

Related Least Common Multiples of 1314

Frequently Asked Questions on LCM of 1309 and 1314

1. What is the LCM of 1309 and 1314?

Answer: LCM of 1309 and 1314 is 1720026.

2. What are the Factors of 1309?

Answer: Factors of 1309 are 1, 7, 11, 17, 77, 119, 187, 1309. There are 8 integers that are factors of 1309. The greatest factor of 1309 is 1309.

3. What are the Factors of 1314?

Answer: Factors of 1314 are 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314. There are 12 integers that are factors of 1314. The greatest factor of 1314 is 1314.

4. How to Find the LCM of 1309 and 1314?

Answer:

Least Common Multiple of 1309 and 1314 = 1720026

Step 1: Find the prime factorization of 1309

1309 = 7 x 11 x 17

Step 2: Find the prime factorization of 1314

1314 = 2 x 3 x 3 x 73

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

LCM = 1720026 = 2 x 3 x 3 x 7 x 11 x 17 x 73

Step 4: Therefore, the least common multiple of 1309 and 1314 is 1720026.