Least Common Multiple of 10300 and 10304

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10300 and 10304 the smallest integer that is 26532800 that is divisible by both numbers.

Least Common Multiple (LCM) of 10300 and 10304 is 26532800.

LCM(10300,10304) = 26532800

LCM of 10300 and 10304

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

LCM of:
and

Least Common Multiple of 10300 and 10304

LCM of 10300 and 10304 is 26532800

Least common multiple can be found by multiplying the highest exponent prime factors of 10300 and 10304. First we will calculate the prime factors of 10300 and 10304.

Prime Factorization of 10300


2 10300
2 5150
5 2575
5 515
103 103
1

Prime factors of 10300 are 2, 5,103. Prime factorization of 10300 in exponential form is:

10300 = 22×52×1031

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

Now multiplying the highest exponent prime factors to calculate the LCM of 10300 and 10304.

LCM(10300,10304) = 26×52×71×231×1031
LCM(10300,10304) = 26532800

Factors of 10300

List of positive integer factors of 10300 that divides 10300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 103, 206, 412, 515, 1030, 2060, 2575, 5150, 10300

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

Least Common Multiple of 10300 and 10304 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10300 and 10304, than apply into the LCM equation.

GCF(10300,10304) = 4
LCM(10300,10304) = ( 10300 × 10304) / 4
LCM(10300,10304) = 106131200 / 4
LCM(10300,10304) = 26532800

Properties of LCM 10300 and 10304

(i) The LCM of 10304 and 10300 is associative

LCM of 10300 and 10304 = LCM of 10304 and 10300

Related Least Common Multiples of 10300

Related Least Common Multiples of 10304

Frequently Asked Questions on LCM of 10300 and 10304

1. What is the LCM of 10300 and 10304?

Answer: LCM of 10300 and 10304 is 26532800.

2. What are the Factors of 10300?

Answer: Factors of 10300 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 103, 206, 412, 515, 1030, 2060, 2575, 5150, 10300. There are 18 integers that are factors of 10300. The greatest factor of 10300 is 10300.

3. 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.

4. How to Find the LCM of 10300 and 10304?

Answer:

Least Common Multiple of 10300 and 10304 = 26532800

Step 1: Find the prime factorization of 10300

10300 = 2 x 2 x 5 x 5 x 103

Step 2: Find the prime factorization of 10304

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

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

LCM = 26532800 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 7 x 23 x 103

Step 4: Therefore, the least common multiple of 10300 and 10304 is 26532800.