Least Common Multiple of 1305 and 1312

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 1312 the smallest integer that is 1712160 that is divisible by both numbers.

Least Common Multiple (LCM) of 1305 and 1312 is 1712160.

LCM(1305,1312) = 1712160

LCM of 1305 and 1312

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

LCM of:
and

Least Common Multiple of 1305 and 1312

LCM of 1305 and 1312 is 1712160

Least common multiple can be found by multiplying the highest exponent prime factors of 1305 and 1312. First we will calculate the prime factors of 1305 and 1312.

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 1312


2 1312
2 656
2 328
2 164
2 82
41 41
1

Prime factors of 1312 are 2,41. Prime factorization of 1312 in exponential form is:

1312 = 25×411

Now multiplying the highest exponent prime factors to calculate the LCM of 1305 and 1312.

LCM(1305,1312) = 25×32×51×291×411
LCM(1305,1312) = 1712160

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 1312

List of positive integer factors of 1312 that divides 1312 without a remainder.

1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656, 1312

Least Common Multiple of 1305 and 1312 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 1312, than apply into the LCM equation.

GCF(1305,1312) = 1
LCM(1305,1312) = ( 1305 × 1312) / 1
LCM(1305,1312) = 1712160 / 1
LCM(1305,1312) = 1712160

Properties of LCM 1305 and 1312

(i) The LCM of 1312 and 1305 is associative

LCM of 1305 and 1312 = LCM of 1312 and 1305

Related Least Common Multiples of 1305

Related Least Common Multiples of 1312

Frequently Asked Questions on LCM of 1305 and 1312

1. What is the LCM of 1305 and 1312?

Answer: LCM of 1305 and 1312 is 1712160.

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 1312?

Answer: Factors of 1312 are 1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656, 1312. There are 12 integers that are factors of 1312. The greatest factor of 1312 is 1312.

4. How to Find the LCM of 1305 and 1312?

Answer:

Least Common Multiple of 1305 and 1312 = 1712160

Step 1: Find the prime factorization of 1305

1305 = 3 x 3 x 5 x 29

Step 2: Find the prime factorization of 1312

1312 = 2 x 2 x 2 x 2 x 2 x 41

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

LCM = 1712160 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 29 x 41

Step 4: Therefore, the least common multiple of 1305 and 1312 is 1712160.