Least Common Multiple of 2106 and 2110

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2106 and 2110 the smallest integer that is 2221830 that is divisible by both numbers.

Least Common Multiple (LCM) of 2106 and 2110 is 2221830.

LCM(2106,2110) = 2221830

LCM of 2106 and 2110

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

LCM of:
and

Least Common Multiple of 2106 and 2110

LCM of 2106 and 2110 is 2221830

Least common multiple can be found by multiplying the highest exponent prime factors of 2106 and 2110. First we will calculate the prime factors of 2106 and 2110.

Prime Factorization of 2106


2 2106
3 1053
3 351
3 117
3 39
13 13
1

Prime factors of 2106 are 2, 3,13. Prime factorization of 2106 in exponential form is:

2106 = 21×34×131

Prime Factorization of 2110


2 2110
5 1055
211 211
1

Prime factors of 2110 are 2, 5,211. Prime factorization of 2110 in exponential form is:

2110 = 21×51×2111

Now multiplying the highest exponent prime factors to calculate the LCM of 2106 and 2110.

LCM(2106,2110) = 21×34×51×131×2111
LCM(2106,2110) = 2221830

Factors of 2106

List of positive integer factors of 2106 that divides 2106 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106

Factors of 2110

List of positive integer factors of 2110 that divides 2110 without a remainder.

1, 2, 5, 10, 211, 422, 1055, 2110

Least Common Multiple of 2106 and 2110 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2106 and 2110, than apply into the LCM equation.

GCF(2106,2110) = 2
LCM(2106,2110) = ( 2106 × 2110) / 2
LCM(2106,2110) = 4443660 / 2
LCM(2106,2110) = 2221830

Properties of LCM 2106 and 2110

(i) The LCM of 2110 and 2106 is associative

LCM of 2106 and 2110 = LCM of 2110 and 2106

Related Least Common Multiples of 2106

Related Least Common Multiples of 2110

Frequently Asked Questions on LCM of 2106 and 2110

1. What is the LCM of 2106 and 2110?

Answer: LCM of 2106 and 2110 is 2221830.

2. What are the Factors of 2106?

Answer: Factors of 2106 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106. There are 20 integers that are factors of 2106. The greatest factor of 2106 is 2106.

3. What are the Factors of 2110?

Answer: Factors of 2110 are 1, 2, 5, 10, 211, 422, 1055, 2110. There are 8 integers that are factors of 2110. The greatest factor of 2110 is 2110.

4. How to Find the LCM of 2106 and 2110?

Answer:

Least Common Multiple of 2106 and 2110 = 2221830

Step 1: Find the prime factorization of 2106

2106 = 2 x 3 x 3 x 3 x 3 x 13

Step 2: Find the prime factorization of 2110

2110 = 2 x 5 x 211

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

LCM = 2221830 = 2 x 3 x 3 x 3 x 3 x 5 x 13 x 211

Step 4: Therefore, the least common multiple of 2106 and 2110 is 2221830.