Least Common Multiple of 2109 and 2116

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 2116 the smallest integer that is 4462644 that is divisible by both numbers.

Least Common Multiple (LCM) of 2109 and 2116 is 4462644.

LCM(2109,2116) = 4462644

LCM of 2109 and 2116

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

LCM of:
and

Least Common Multiple of 2109 and 2116

LCM of 2109 and 2116 is 4462644

Least common multiple can be found by multiplying the highest exponent prime factors of 2109 and 2116. First we will calculate the prime factors of 2109 and 2116.

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 2116


2 2116
2 1058
23 529
23 23
1

Prime factors of 2116 are 2,23. Prime factorization of 2116 in exponential form is:

2116 = 22×232

Now multiplying the highest exponent prime factors to calculate the LCM of 2109 and 2116.

LCM(2109,2116) = 22×31×191×232×371
LCM(2109,2116) = 4462644

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 2116

List of positive integer factors of 2116 that divides 2116 without a remainder.

1, 2, 4, 23, 46, 92, 529, 1058, 2116

Least Common Multiple of 2109 and 2116 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 2116, than apply into the LCM equation.

GCF(2109,2116) = 1
LCM(2109,2116) = ( 2109 × 2116) / 1
LCM(2109,2116) = 4462644 / 1
LCM(2109,2116) = 4462644

Properties of LCM 2109 and 2116

(i) The LCM of 2116 and 2109 is associative

LCM of 2109 and 2116 = LCM of 2116 and 2109

Related Least Common Multiples of 2109

Related Least Common Multiples of 2116

Frequently Asked Questions on LCM of 2109 and 2116

1. What is the LCM of 2109 and 2116?

Answer: LCM of 2109 and 2116 is 4462644.

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 2116?

Answer: Factors of 2116 are 1, 2, 4, 23, 46, 92, 529, 1058, 2116. There are 9 integers that are factors of 2116. The greatest factor of 2116 is 2116.

4. How to Find the LCM of 2109 and 2116?

Answer:

Least Common Multiple of 2109 and 2116 = 4462644

Step 1: Find the prime factorization of 2109

2109 = 3 x 19 x 37

Step 2: Find the prime factorization of 2116

2116 = 2 x 2 x 23 x 23

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

LCM = 4462644 = 2 x 2 x 3 x 19 x 23 x 23 x 37

Step 4: Therefore, the least common multiple of 2109 and 2116 is 4462644.