Least Common Multiple of 1302 and 1305

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1302 and 1305 the smallest integer that is 566370 that is divisible by both numbers.

Least Common Multiple (LCM) of 1302 and 1305 is 566370.

LCM(1302,1305) = 566370

LCM of 1302 and 1305

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

LCM of:
and

Least Common Multiple of 1302 and 1305

LCM of 1302 and 1305 is 566370

Least common multiple can be found by multiplying the highest exponent prime factors of 1302 and 1305. First we will calculate the prime factors of 1302 and 1305.

Prime Factorization of 1302


2 1302
3 651
7 217
31 31
1

Prime factors of 1302 are 2, 3, 7,31. Prime factorization of 1302 in exponential form is:

1302 = 21×31×71×311

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1302 and 1305.

LCM(1302,1305) = 21×32×51×71×291×311
LCM(1302,1305) = 566370

Factors of 1302

List of positive integer factors of 1302 that divides 1302 without a remainder.

1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302

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

Least Common Multiple of 1302 and 1305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1302 and 1305, than apply into the LCM equation.

GCF(1302,1305) = 3
LCM(1302,1305) = ( 1302 × 1305) / 3
LCM(1302,1305) = 1699110 / 3
LCM(1302,1305) = 566370

Properties of LCM 1302 and 1305

(i) The LCM of 1305 and 1302 is associative

LCM of 1302 and 1305 = LCM of 1305 and 1302

Related Least Common Multiples of 1302

Related Least Common Multiples of 1305

Frequently Asked Questions on LCM of 1302 and 1305

1. What is the LCM of 1302 and 1305?

Answer: LCM of 1302 and 1305 is 566370.

2. What are the Factors of 1302?

Answer: Factors of 1302 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302. There are 16 integers that are factors of 1302. The greatest factor of 1302 is 1302.

3. 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.

4. How to Find the LCM of 1302 and 1305?

Answer:

Least Common Multiple of 1302 and 1305 = 566370

Step 1: Find the prime factorization of 1302

1302 = 2 x 3 x 7 x 31

Step 2: Find the prime factorization of 1305

1305 = 3 x 3 x 5 x 29

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

LCM = 566370 = 2 x 3 x 3 x 5 x 7 x 29 x 31

Step 4: Therefore, the least common multiple of 1302 and 1305 is 566370.