Least Common Multiple of 2104 and 2106

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2104 and 2106 the smallest integer that is 2215512 that is divisible by both numbers.

Least Common Multiple (LCM) of 2104 and 2106 is 2215512.

LCM(2104,2106) = 2215512

LCM of 2104 and 2106

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

LCM of:
and

Least Common Multiple of 2104 and 2106

LCM of 2104 and 2106 is 2215512

Least common multiple can be found by multiplying the highest exponent prime factors of 2104 and 2106. First we will calculate the prime factors of 2104 and 2106.

Prime Factorization of 2104


2 2104
2 1052
2 526
263 263
1

Prime factors of 2104 are 2,263. Prime factorization of 2104 in exponential form is:

2104 = 23×2631

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

Now multiplying the highest exponent prime factors to calculate the LCM of 2104 and 2106.

LCM(2104,2106) = 23×34×131×2631
LCM(2104,2106) = 2215512

Factors of 2104

List of positive integer factors of 2104 that divides 2104 without a remainder.

1, 2, 4, 8, 263, 526, 1052, 2104

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

Least Common Multiple of 2104 and 2106 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2104 and 2106, than apply into the LCM equation.

GCF(2104,2106) = 2
LCM(2104,2106) = ( 2104 × 2106) / 2
LCM(2104,2106) = 4431024 / 2
LCM(2104,2106) = 2215512

Properties of LCM 2104 and 2106

(i) The LCM of 2106 and 2104 is associative

LCM of 2104 and 2106 = LCM of 2106 and 2104

Related Least Common Multiples of 2104

Related Least Common Multiples of 2106

Frequently Asked Questions on LCM of 2104 and 2106

1. What is the LCM of 2104 and 2106?

Answer: LCM of 2104 and 2106 is 2215512.

2. What are the Factors of 2104?

Answer: Factors of 2104 are 1, 2, 4, 8, 263, 526, 1052, 2104. There are 8 integers that are factors of 2104. The greatest factor of 2104 is 2104.

3. 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.

4. How to Find the LCM of 2104 and 2106?

Answer:

Least Common Multiple of 2104 and 2106 = 2215512

Step 1: Find the prime factorization of 2104

2104 = 2 x 2 x 2 x 263

Step 2: Find the prime factorization of 2106

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

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

LCM = 2215512 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 13 x 263

Step 4: Therefore, the least common multiple of 2104 and 2106 is 2215512.