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;
- Least Common Multiple of 102 and 109 by Prime method
- Least Common Multiple of 102 and 109 with GCF Formula
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.
