Least Common Multiple of 102 and 109

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 109 the smallest integer that is 11118 that is divisible by both numbers.

Least Common Multiple (LCM) of 102 and 109 is 11118.

LCM(102,109) = 11118

LCM of 102 and 109

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

LCM of:
and

Least Common Multiple of 102 and 109

LCM of 102 and 109 is 11118

Least common multiple can be found by multiplying the highest exponent prime factors of 102 and 109. First we will calculate the prime factors of 102 and 109.

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 109


109 109
1

Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:

109 = 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 102 and 109.

LCM(102,109) = 21×31×171×1091
LCM(102,109) = 11118

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 109

List of positive integer factors of 109 that divides 109 without a remainder.

1, 109

Least Common Multiple of 102 and 109 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 109, than apply into the LCM equation.

GCF(102,109) = 1
LCM(102,109) = ( 102 × 109) / 1
LCM(102,109) = 11118 / 1
LCM(102,109) = 11118

Properties of LCM 102 and 109

(i) The LCM of 109 and 102 is associative

LCM of 102 and 109 = LCM of 109 and 102

Related Least Common Multiples of 102

Related Least Common Multiples of 109

Frequently Asked Questions on LCM of 102 and 109

1. What is the LCM of 102 and 109?

Answer: LCM of 102 and 109 is 11118.

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 109?

Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.

4. How to Find the LCM of 102 and 109?

Answer:

Least Common Multiple of 102 and 109 = 11118

Step 1: Find the prime factorization of 102

102 = 2 x 3 x 17

Step 2: Find the prime factorization of 109

109 = 109

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

LCM = 11118 = 2 x 3 x 17 x 109

Step 4: Therefore, the least common multiple of 102 and 109 is 11118.