Least Common Multiple of 10300 and 10302

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 10302 the smallest integer that is 53055300 that is divisible by both numbers.

Least Common Multiple (LCM) of 10300 and 10302 is 53055300.

LCM(10300,10302) = 53055300

LCM of 10300 and 10302

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

LCM of:
and

Least Common Multiple of 10300 and 10302

LCM of 10300 and 10302 is 53055300

Least common multiple can be found by multiplying the highest exponent prime factors of 10300 and 10302. First we will calculate the prime factors of 10300 and 10302.

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 10302


2 10302
3 5151
17 1717
101 101
1

Prime factors of 10302 are 2, 3, 17,101. Prime factorization of 10302 in exponential form is:

10302 = 21×31×171×1011

Now multiplying the highest exponent prime factors to calculate the LCM of 10300 and 10302.

LCM(10300,10302) = 22×31×52×171×1011×1031
LCM(10300,10302) = 53055300

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 10302

List of positive integer factors of 10302 that divides 10302 without a remainder.

1, 2, 3, 6, 17, 34, 51, 101, 102, 202, 303, 606, 1717, 3434, 5151, 10302

Least Common Multiple of 10300 and 10302 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 10302, than apply into the LCM equation.

GCF(10300,10302) = 2
LCM(10300,10302) = ( 10300 × 10302) / 2
LCM(10300,10302) = 106110600 / 2
LCM(10300,10302) = 53055300

Properties of LCM 10300 and 10302

(i) The LCM of 10302 and 10300 is associative

LCM of 10300 and 10302 = LCM of 10302 and 10300

Related Least Common Multiples of 10300

Related Least Common Multiples of 10302

Frequently Asked Questions on LCM of 10300 and 10302

1. What is the LCM of 10300 and 10302?

Answer: LCM of 10300 and 10302 is 53055300.

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 10302?

Answer: Factors of 10302 are 1, 2, 3, 6, 17, 34, 51, 101, 102, 202, 303, 606, 1717, 3434, 5151, 10302. There are 16 integers that are factors of 10302. The greatest factor of 10302 is 10302.

4. How to Find the LCM of 10300 and 10302?

Answer:

Least Common Multiple of 10300 and 10302 = 53055300

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 10302

10302 = 2 x 3 x 17 x 101

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

LCM = 53055300 = 2 x 2 x 3 x 5 x 5 x 17 x 101 x 103

Step 4: Therefore, the least common multiple of 10300 and 10302 is 53055300.