Least Common Multiple of 102 and 107

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 102 and 107 the smallest integer that is 10914 that is divisible by both numbers.

Least Common Multiple (LCM) of 102 and 107 is 10914.

LCM(102,107) = 10914

LCM of 102 and 107

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

LCM of:
and

Least Common Multiple of 102 and 107

LCM of 102 and 107 is 10914

Least common multiple can be found by multiplying the highest exponent prime factors of 102 and 107. First we will calculate the prime factors of 102 and 107.

Prime Factorization of 102


2 102
3 51
17 17
1

Prime factors of 102 are 2, 3,17. Prime factorization of 102 in exponential form is:

102 = 21×31×171

Prime Factorization of 107


107 107
1

Prime factors of 107 are 107. Prime factorization of 107 in exponential form is:

107 = 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 102 and 107.

LCM(102,107) = 21×31×171×1071
LCM(102,107) = 10914

Factors of 102

List of positive integer factors of 102 that divides 102 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102

Factors of 107

List of positive integer factors of 107 that divides 107 without a remainder.

1, 107

Least Common Multiple of 102 and 107 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 102 and 107, than apply into the LCM equation.

GCF(102,107) = 1
LCM(102,107) = ( 102 × 107) / 1
LCM(102,107) = 10914 / 1
LCM(102,107) = 10914

Properties of LCM 102 and 107

(i) The LCM of 107 and 102 is associative

LCM of 102 and 107 = LCM of 107 and 102

Related Least Common Multiples of 102

Related Least Common Multiples of 107

Frequently Asked Questions on LCM of 102 and 107

1. What is the LCM of 102 and 107?

Answer: LCM of 102 and 107 is 10914.

2. What are the Factors of 102?

Answer: Factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102. There are 8 integers that are factors of 102. The greatest factor of 102 is 102.

3. What are the Factors of 107?

Answer: Factors of 107 are 1, 107. There are 2 integers that are factors of 107. The greatest factor of 107 is 107.

4. How to Find the LCM of 102 and 107?

Answer:

Least Common Multiple of 102 and 107 = 10914

Step 1: Find the prime factorization of 102

102 = 2 x 3 x 17

Step 2: Find the prime factorization of 107

107 = 107

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

LCM = 10914 = 2 x 3 x 17 x 107

Step 4: Therefore, the least common multiple of 102 and 107 is 10914.