Least Common Multiple of 2109 and 2117
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2109 and 2117 the smallest integer that is 4464753 that is divisible by both numbers.
Least Common Multiple (LCM) of 2109 and 2117 is 4464753.
LCM(2109,2117) = 4464753
LCM of 2109 and 2117
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2109 and 2117 by Prime method
- Least Common Multiple of 2109 and 2117 with GCF Formula
LCM of 2109 and 2117 is 4464753
Least common multiple can be found by multiplying the highest exponent prime factors of 2109 and 2117. First we will calculate the prime factors of 2109 and 2117.
Prime Factorization of 2109
| 3 | 2109 |
| 19 | 703 |
| 37 | 37 |
| 1 |
Prime factors of 2109 are 3, 19,37. Prime factorization of 2109 in exponential form is:
2109 = 31×191×371
Prime Factorization of 2117
| 29 | 2117 |
| 73 | 73 |
| 1 |
Prime factors of 2117 are 29,73. Prime factorization of 2117 in exponential form is:
2117 = 291×731
Now multiplying the highest exponent prime factors to calculate the LCM of 2109 and 2117.
LCM(2109,2117) = 31×191×291×371×731
LCM(2109,2117) = 4464753
Factors of 2109
List of positive integer factors of 2109 that divides 2109 without a remainder.
1, 3, 19, 37, 57, 111, 703, 2109
Factors of 2117
List of positive integer factors of 2117 that divides 2117 without a remainder.
1, 29, 73, 2117
Least Common Multiple of 2109 and 2117 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2109 and 2117, than apply into the LCM equation.
GCF(2109,2117) = 1
LCM(2109,2117) = ( 2109 × 2117) / 1
LCM(2109,2117) = 4464753 / 1
LCM(2109,2117) = 4464753
Properties of LCM 2109 and 2117
(i) The LCM of 2117 and 2109 is associative
LCM of 2109 and 2117 = LCM of 2117 and 2109
Related Least Common Multiples of 2109
Related Least Common Multiples of 2117
Frequently Asked Questions on LCM of 2109 and 2117
1. What is the LCM of 2109 and 2117?
Answer: LCM of 2109 and 2117 is 4464753.
2. What are the Factors of 2109?
Answer: Factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109. There are 8 integers that are factors of 2109. The greatest factor of 2109 is 2109.
3. What are the Factors of 2117?
Answer: Factors of 2117 are 1, 29, 73, 2117. There are 4 integers that are factors of 2117. The greatest factor of 2117 is 2117.
4. How to Find the LCM of 2109 and 2117?
Answer:
Least Common Multiple of 2109 and 2117 = 4464753
Step 1: Find the prime factorization of 2109
2109 = 3 x 19 x 37
Step 2: Find the prime factorization of 2117
2117 = 29 x 73
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4464753 = 3 x 19 x 29 x 37 x 73
Step 4: Therefore, the least common multiple of 2109 and 2117 is 4464753.