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
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
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
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
(i) The LCM of 2106 and 2104 is associative
LCM of 2104 and 2106 = LCM of 2106 and 2104
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.