Least Common Multiple of 109 and 114
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 114 the smallest integer that is 12426 that is divisible by both numbers.
Least Common Multiple (LCM) of 109 and 114 is 12426.
LCM(109,114) = 12426
LCM of 109 and 114
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 109 and 114 by Prime method
- Least Common Multiple of 109 and 114 with GCF Formula
LCM of 109 and 114 is 12426
Least common multiple can be found by multiplying the highest exponent prime factors of 109 and 114. First we will calculate the prime factors of 109 and 114.
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 114
| 2 | 114 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 114 are 2, 3,19. Prime factorization of 114 in exponential form is:
114 = 21×31×191
Now multiplying the highest exponent prime factors to calculate the LCM of 109 and 114.
LCM(109,114) = 21×31×191×1091
LCM(109,114) = 12426
Factors of 109
List of positive integer factors of 109 that divides 109 without a remainder.
1, 109
Factors of 114
List of positive integer factors of 114 that divides 114 without a remainder.
1, 2, 3, 6, 19, 38, 57, 114
Least Common Multiple of 109 and 114 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 114, than apply into the LCM equation.
GCF(109,114) = 1
LCM(109,114) = ( 109 × 114) / 1
LCM(109,114) = 12426 / 1
LCM(109,114) = 12426
Properties of LCM 109 and 114
(i) The LCM of 114 and 109 is associative
LCM of 109 and 114 = LCM of 114 and 109
Related Least Common Multiples of 109
Related Least Common Multiples of 114
Frequently Asked Questions on LCM of 109 and 114
1. What is the LCM of 109 and 114?
Answer: LCM of 109 and 114 is 12426.
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 114?
Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.
4. How to Find the LCM of 109 and 114?
Answer:
Least Common Multiple of 109 and 114 = 12426
Step 1: Find the prime factorization of 109
109 = 109
Step 2: Find the prime factorization of 114
114 = 2 x 3 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12426 = 2 x 3 x 19 x 109
Step 4: Therefore, the least common multiple of 109 and 114 is 12426.