Least Common Multiple of 10304 and 10310

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10304 and 10310 the smallest integer that is 53117120 that is divisible by both numbers.

Least Common Multiple (LCM) of 10304 and 10310 is 53117120.

LCM(10304,10310) = 53117120

LCM of 10304 and 10310

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

LCM of:
and

Least Common Multiple of 10304 and 10310

LCM of 10304 and 10310 is 53117120

Least common multiple can be found by multiplying the highest exponent prime factors of 10304 and 10310. First we will calculate the prime factors of 10304 and 10310.

Prime Factorization of 10304


2 10304
2 5152
2 2576
2 1288
2 644
2 322
7 161
23 23
1

Prime factors of 10304 are 2, 7,23. Prime factorization of 10304 in exponential form is:

10304 = 26×71×231

Prime Factorization of 10310


2 10310
5 5155
1031 1031
1

Prime factors of 10310 are 2, 5,1031. Prime factorization of 10310 in exponential form is:

10310 = 21×51×10311

Now multiplying the highest exponent prime factors to calculate the LCM of 10304 and 10310.

LCM(10304,10310) = 26×51×71×231×10311
LCM(10304,10310) = 53117120

Factors of 10304

List of positive integer factors of 10304 that divides 10304 without a remainder.

1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 64, 92, 112, 161, 184, 224, 322, 368, 448, 644, 736, 1288, 1472, 2576, 5152, 10304

Factors of 10310

List of positive integer factors of 10310 that divides 10310 without a remainder.

1, 2, 5, 10, 1031, 2062, 5155, 10310

Least Common Multiple of 10304 and 10310 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10304 and 10310, than apply into the LCM equation.

GCF(10304,10310) = 2
LCM(10304,10310) = ( 10304 × 10310) / 2
LCM(10304,10310) = 106234240 / 2
LCM(10304,10310) = 53117120

Properties of LCM 10304 and 10310

(i) The LCM of 10310 and 10304 is associative

LCM of 10304 and 10310 = LCM of 10310 and 10304

Related Least Common Multiples of 10304

Related Least Common Multiples of 10310

Frequently Asked Questions on LCM of 10304 and 10310

1. What is the LCM of 10304 and 10310?

Answer: LCM of 10304 and 10310 is 53117120.

2. What are the Factors of 10304?

Answer: Factors of 10304 are 1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 64, 92, 112, 161, 184, 224, 322, 368, 448, 644, 736, 1288, 1472, 2576, 5152, 10304. There are 28 integers that are factors of 10304. The greatest factor of 10304 is 10304.

3. What are the Factors of 10310?

Answer: Factors of 10310 are 1, 2, 5, 10, 1031, 2062, 5155, 10310. There are 8 integers that are factors of 10310. The greatest factor of 10310 is 10310.

4. How to Find the LCM of 10304 and 10310?

Answer:

Least Common Multiple of 10304 and 10310 = 53117120

Step 1: Find the prime factorization of 10304

10304 = 2 x 2 x 2 x 2 x 2 x 2 x 7 x 23

Step 2: Find the prime factorization of 10310

10310 = 2 x 5 x 1031

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

LCM = 53117120 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 7 x 23 x 1031

Step 4: Therefore, the least common multiple of 10304 and 10310 is 53117120.