Least Common Multiple of 2109 and 2114

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 2114 the smallest integer that is 4458426 that is divisible by both numbers.

Least Common Multiple (LCM) of 2109 and 2114 is 4458426.

LCM(2109,2114) = 4458426

LCM of 2109 and 2114

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 2109 and 2114

LCM of 2109 and 2114 is 4458426

Least common multiple can be found by multiplying the highest exponent prime factors of 2109 and 2114. First we will calculate the prime factors of 2109 and 2114.

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 2114


2 2114
7 1057
151 151
1

Prime factors of 2114 are 2, 7,151. Prime factorization of 2114 in exponential form is:

2114 = 21×71×1511

Now multiplying the highest exponent prime factors to calculate the LCM of 2109 and 2114.

LCM(2109,2114) = 21×31×71×191×371×1511
LCM(2109,2114) = 4458426

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 2114

List of positive integer factors of 2114 that divides 2114 without a remainder.

1, 2, 7, 14, 151, 302, 1057, 2114

Least Common Multiple of 2109 and 2114 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 2114, than apply into the LCM equation.

GCF(2109,2114) = 1
LCM(2109,2114) = ( 2109 × 2114) / 1
LCM(2109,2114) = 4458426 / 1
LCM(2109,2114) = 4458426

Properties of LCM 2109 and 2114

(i) The LCM of 2114 and 2109 is associative

LCM of 2109 and 2114 = LCM of 2114 and 2109

Related Least Common Multiples of 2109

Related Least Common Multiples of 2114

Frequently Asked Questions on LCM of 2109 and 2114

1. What is the LCM of 2109 and 2114?

Answer: LCM of 2109 and 2114 is 4458426.

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 2114?

Answer: Factors of 2114 are 1, 2, 7, 14, 151, 302, 1057, 2114. There are 8 integers that are factors of 2114. The greatest factor of 2114 is 2114.

4. How to Find the LCM of 2109 and 2114?

Answer:

Least Common Multiple of 2109 and 2114 = 4458426

Step 1: Find the prime factorization of 2109

2109 = 3 x 19 x 37

Step 2: Find the prime factorization of 2114

2114 = 2 x 7 x 151

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 4458426 = 2 x 3 x 7 x 19 x 37 x 151

Step 4: Therefore, the least common multiple of 2109 and 2114 is 4458426.