Least Common Multiple of 2101 and 2109
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2101 and 2109 the smallest integer that is 4431009 that is divisible by both numbers.
Least Common Multiple (LCM) of 2101 and 2109 is 4431009.
LCM(2101,2109) = 4431009
LCM of 2101 and 2109
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2101 and 2109 by Prime method
- Least Common Multiple of 2101 and 2109 with GCF Formula
LCM of 2101 and 2109 is 4431009
Least common multiple can be found by multiplying the highest exponent prime factors of 2101 and 2109. First we will calculate the prime factors of 2101 and 2109.
Prime Factorization of 2101
| 11 | 2101 |
| 191 | 191 |
| 1 |
Prime factors of 2101 are 11,191. Prime factorization of 2101 in exponential form is:
2101 = 111×1911
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
Now multiplying the highest exponent prime factors to calculate the LCM of 2101 and 2109.
LCM(2101,2109) = 31×111×191×371×1911
LCM(2101,2109) = 4431009
Factors of 2101
List of positive integer factors of 2101 that divides 2101 without a remainder.
1, 11, 191, 2101
Factors of 2109
List of positive integer factors of 2109 that divides 2109 without a remainder.
1, 3, 19, 37, 57, 111, 703, 2109
Least Common Multiple of 2101 and 2109 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2101 and 2109, than apply into the LCM equation.
GCF(2101,2109) = 1
LCM(2101,2109) = ( 2101 × 2109) / 1
LCM(2101,2109) = 4431009 / 1
LCM(2101,2109) = 4431009
Properties of LCM 2101 and 2109
(i) The LCM of 2109 and 2101 is associative
LCM of 2101 and 2109 = LCM of 2109 and 2101
Related Least Common Multiples of 2101
Related Least Common Multiples of 2109
Frequently Asked Questions on LCM of 2101 and 2109
1. What is the LCM of 2101 and 2109?
Answer: LCM of 2101 and 2109 is 4431009.
2. What are the Factors of 2101?
Answer: Factors of 2101 are 1, 11, 191, 2101. There are 4 integers that are factors of 2101. The greatest factor of 2101 is 2101.
3. 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.
4. How to Find the LCM of 2101 and 2109?
Answer:
Least Common Multiple of 2101 and 2109 = 4431009
Step 1: Find the prime factorization of 2101
2101 = 11 x 191
Step 2: Find the prime factorization of 2109
2109 = 3 x 19 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 = 4431009 = 3 x 11 x 19 x 37 x 191
Step 4: Therefore, the least common multiple of 2101 and 2109 is 4431009.