Least Common Multiple of 10102 and 10110

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10102 and 10110 the smallest integer that is 51065610 that is divisible by both numbers.

Least Common Multiple (LCM) of 10102 and 10110 is 51065610.

LCM(10102,10110) = 51065610

LCM of 10102 and 10110

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

LCM of:
and

Least Common Multiple of 10102 and 10110

LCM of 10102 and 10110 is 51065610

Least common multiple can be found by multiplying the highest exponent prime factors of 10102 and 10110. First we will calculate the prime factors of 10102 and 10110.

Prime Factorization of 10102


2 10102
5051 5051
1

Prime factors of 10102 are 2,5051. Prime factorization of 10102 in exponential form is:

10102 = 21×50511

Prime Factorization of 10110


2 10110
3 5055
5 1685
337 337
1

Prime factors of 10110 are 2, 3, 5,337. Prime factorization of 10110 in exponential form is:

10110 = 21×31×51×3371

Now multiplying the highest exponent prime factors to calculate the LCM of 10102 and 10110.

LCM(10102,10110) = 21×31×51×3371×50511
LCM(10102,10110) = 51065610

Factors of 10102

List of positive integer factors of 10102 that divides 10102 without a remainder.

1, 2, 5051, 10102

Factors of 10110

List of positive integer factors of 10110 that divides 10110 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 337, 674, 1011, 1685, 2022, 3370, 5055, 10110

Least Common Multiple of 10102 and 10110 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10102 and 10110, than apply into the LCM equation.

GCF(10102,10110) = 2
LCM(10102,10110) = ( 10102 × 10110) / 2
LCM(10102,10110) = 102131220 / 2
LCM(10102,10110) = 51065610

Properties of LCM 10102 and 10110

(i) The LCM of 10110 and 10102 is associative

LCM of 10102 and 10110 = LCM of 10110 and 10102

Related Least Common Multiples of 10102

Related Least Common Multiples of 10110

Frequently Asked Questions on LCM of 10102 and 10110

1. What is the LCM of 10102 and 10110?

Answer: LCM of 10102 and 10110 is 51065610.

2. What are the Factors of 10102?

Answer: Factors of 10102 are 1, 2, 5051, 10102. There are 4 integers that are factors of 10102. The greatest factor of 10102 is 10102.

3. What are the Factors of 10110?

Answer: Factors of 10110 are 1, 2, 3, 5, 6, 10, 15, 30, 337, 674, 1011, 1685, 2022, 3370, 5055, 10110. There are 16 integers that are factors of 10110. The greatest factor of 10110 is 10110.

4. How to Find the LCM of 10102 and 10110?

Answer:

Least Common Multiple of 10102 and 10110 = 51065610

Step 1: Find the prime factorization of 10102

10102 = 2 x 5051

Step 2: Find the prime factorization of 10110

10110 = 2 x 3 x 5 x 337

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

LCM = 51065610 = 2 x 3 x 5 x 337 x 5051

Step 4: Therefore, the least common multiple of 10102 and 10110 is 51065610.