Least Common Multiple of 1305 and 1309

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1305 and 1309 the smallest integer that is 1708245 that is divisible by both numbers.

Least Common Multiple (LCM) of 1305 and 1309 is 1708245.

LCM(1305,1309) = 1708245

LCM of 1305 and 1309

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

LCM of:
and

Least Common Multiple of 1305 and 1309

LCM of 1305 and 1309 is 1708245

Least common multiple can be found by multiplying the highest exponent prime factors of 1305 and 1309. First we will calculate the prime factors of 1305 and 1309.

Prime Factorization of 1305


3 1305
3 435
5 145
29 29
1

Prime factors of 1305 are 3, 5,29. Prime factorization of 1305 in exponential form is:

1305 = 32×51×291

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1305 and 1309.

LCM(1305,1309) = 32×51×71×111×171×291
LCM(1305,1309) = 1708245

Factors of 1305

List of positive integer factors of 1305 that divides 1305 without a remainder.

1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 1305

Factors of 1309

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

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

Least Common Multiple of 1305 and 1309 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1305 and 1309, than apply into the LCM equation.

GCF(1305,1309) = 1
LCM(1305,1309) = ( 1305 × 1309) / 1
LCM(1305,1309) = 1708245 / 1
LCM(1305,1309) = 1708245

Properties of LCM 1305 and 1309

(i) The LCM of 1309 and 1305 is associative

LCM of 1305 and 1309 = LCM of 1309 and 1305

Related Least Common Multiples of 1305

Related Least Common Multiples of 1309

Frequently Asked Questions on LCM of 1305 and 1309

1. What is the LCM of 1305 and 1309?

Answer: LCM of 1305 and 1309 is 1708245.

2. What are the Factors of 1305?

Answer: Factors of 1305 are 1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 1305. There are 12 integers that are factors of 1305. The greatest factor of 1305 is 1305.

3. 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.

4. How to Find the LCM of 1305 and 1309?

Answer:

Least Common Multiple of 1305 and 1309 = 1708245

Step 1: Find the prime factorization of 1305

1305 = 3 x 3 x 5 x 29

Step 2: Find the prime factorization of 1309

1309 = 7 x 11 x 17

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

LCM = 1708245 = 3 x 3 x 5 x 7 x 11 x 17 x 29

Step 4: Therefore, the least common multiple of 1305 and 1309 is 1708245.