Least Common Multiple of 109 and 111
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 109 and 111 the smallest integer that is 12099 that is divisible by both numbers.
Least Common Multiple (LCM) of 109 and 111 is 12099.
LCM(109,111) = 12099
LCM of 109 and 111
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 109 and 111 by Prime method
- Least Common Multiple of 109 and 111 with GCF Formula
LCM of 109 and 111 is 12099
Least common multiple can be found by multiplying the highest exponent prime factors of 109 and 111. First we will calculate the prime factors of 109 and 111.
Prime Factorization of 109
| 109 | 109 |
| 1 |
Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:
109 = 1091
Prime Factorization of 111
| 3 | 111 |
| 37 | 37 |
| 1 |
Prime factors of 111 are 3,37. Prime factorization of 111 in exponential form is:
111 = 31×371
Now multiplying the highest exponent prime factors to calculate the LCM of 109 and 111.
LCM(109,111) = 31×371×1091
LCM(109,111) = 12099
Factors of 109
List of positive integer factors of 109 that divides 109 without a remainder.
1, 109
Factors of 111
List of positive integer factors of 111 that divides 111 without a remainder.
1, 3, 37, 111
Least Common Multiple of 109 and 111 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 109 and 111, than apply into the LCM equation.
GCF(109,111) = 1
LCM(109,111) = ( 109 × 111) / 1
LCM(109,111) = 12099 / 1
LCM(109,111) = 12099
Properties of LCM 109 and 111
(i) The LCM of 111 and 109 is associative
LCM of 109 and 111 = LCM of 111 and 109
Related Least Common Multiples of 109
Related Least Common Multiples of 111
Frequently Asked Questions on LCM of 109 and 111
1. What is the LCM of 109 and 111?
Answer: LCM of 109 and 111 is 12099.
2. 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.
3. What are the Factors of 111?
Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.
4. How to Find the LCM of 109 and 111?
Answer:
Least Common Multiple of 109 and 111 = 12099
Step 1: Find the prime factorization of 109
109 = 109
Step 2: Find the prime factorization of 111
111 = 3 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12099 = 3 x 37 x 109
Step 4: Therefore, the least common multiple of 109 and 111 is 12099.