Least Common Multiple of 108 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 108 and 109 the smallest integer that is 11772 that is divisible by both numbers.
Least Common Multiple (LCM) of 108 and 109 is 11772.
LCM(108,109) = 11772
LCM of 108 and 109
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 108 and 109 by Prime method
- Least Common Multiple of 108 and 109 with GCF Formula
LCM of 108 and 109 is 11772
Least common multiple can be found by multiplying the highest exponent prime factors of 108 and 109. First we will calculate the prime factors of 108 and 109.
Prime Factorization of 108
| 2 | 108 |
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 108 are 2,3. Prime factorization of 108 in exponential form is:
108 = 22×33
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 108 and 109.
LCM(108,109) = 22×33×1091
LCM(108,109) = 11772
Factors of 108
List of positive integer factors of 108 that divides 108 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 109
List of positive integer factors of 109 that divides 109 without a remainder.
1, 109
Least Common Multiple of 108 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 108 and 109, than apply into the LCM equation.
GCF(108,109) = 1
LCM(108,109) = ( 108 × 109) / 1
LCM(108,109) = 11772 / 1
LCM(108,109) = 11772
Properties of LCM 108 and 109
(i) The LCM of 109 and 108 is associative
LCM of 108 and 109 = LCM of 109 and 108
Related Least Common Multiples of 108
Related Least Common Multiples of 109
Frequently Asked Questions on LCM of 108 and 109
1. What is the LCM of 108 and 109?
Answer: LCM of 108 and 109 is 11772.
2. What are the Factors of 108?
Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.
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 108 and 109?
Answer:
Least Common Multiple of 108 and 109 = 11772
Step 1: Find the prime factorization of 108
108 = 2 x 2 x 3 x 3 x 3
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 = 11772 = 2 x 2 x 3 x 3 x 3 x 109
Step 4: Therefore, the least common multiple of 108 and 109 is 11772.
