Least Common Multiple of 2108 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 2108 and 2114 the smallest integer that is 2228156 that is divisible by both numbers.

Least Common Multiple (LCM) of 2108 and 2114 is 2228156.

LCM(2108,2114) = 2228156

LCM of 2108 and 2114

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

LCM of:
and

Least Common Multiple of 2108 and 2114

LCM of 2108 and 2114 is 2228156

Least common multiple can be found by multiplying the highest exponent prime factors of 2108 and 2114. First we will calculate the prime factors of 2108 and 2114.

Prime Factorization of 2108


2 2108
2 1054
17 527
31 31
1

Prime factors of 2108 are 2, 17,31. Prime factorization of 2108 in exponential form is:

2108 = 22×171×311

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 2108 and 2114.

LCM(2108,2114) = 22×71×171×311×1511
LCM(2108,2114) = 2228156

Factors of 2108

List of positive integer factors of 2108 that divides 2108 without a remainder.

1, 2, 4, 17, 31, 34, 62, 68, 124, 527, 1054, 2108

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 2108 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 2108 and 2114, than apply into the LCM equation.

GCF(2108,2114) = 2
LCM(2108,2114) = ( 2108 × 2114) / 2
LCM(2108,2114) = 4456312 / 2
LCM(2108,2114) = 2228156

Properties of LCM 2108 and 2114

(i) The LCM of 2114 and 2108 is associative

LCM of 2108 and 2114 = LCM of 2114 and 2108

Related Least Common Multiples of 2108

Related Least Common Multiples of 2114

Frequently Asked Questions on LCM of 2108 and 2114

1. What is the LCM of 2108 and 2114?

Answer: LCM of 2108 and 2114 is 2228156.

2. What are the Factors of 2108?

Answer: Factors of 2108 are 1, 2, 4, 17, 31, 34, 62, 68, 124, 527, 1054, 2108. There are 12 integers that are factors of 2108. The greatest factor of 2108 is 2108.

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 2108 and 2114?

Answer:

Least Common Multiple of 2108 and 2114 = 2228156

Step 1: Find the prime factorization of 2108

2108 = 2 x 2 x 17 x 31

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 = 2228156 = 2 x 2 x 7 x 17 x 31 x 151

Step 4: Therefore, the least common multiple of 2108 and 2114 is 2228156.